Difference between revisions of "MAT1073"

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m (→‎Topics List: Sinmi A. "Edited Prerequisite for each topic to follow the same format")
 
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Students will be able to add, subtract fractions:
+
Students will be able to:
* Determine common denominators and equivalent fractions
+
* Add and subtract fractions.
* Work with proper and improper fractions
+
* Determine common denominators and equivalent fractions.
* Simplify to lowest terms
+
* Work with proper and improper fractions.
 
+
* Simplify to lowest terms.
Students will be able to multiply, and divide fractions:
+
* Multiply and divide fractions.
* Work with proper and improper fractions
 
* Simplify to lowest terms
 
  
 
|-
 
|-
Line 67: Line 65:
 
||
 
||
 
Students will be able to:  
 
Students will be able to:  
* Identify factored vs non-factored forms of a polynomial
+
* Identify factored vs non-factored forms of a polynomial.
* Successfully factor binomials & trinomials and difference of squares into two binomial terms
+
* Successfully factor binomials & trinomials and difference of squares into two binomial terms.
* Factor out GCF
+
* Factor out GCF.
* Multiply and / or distribute to check their factors are correct
+
* Multiply and/or distribute to check their factors are correct.
* Differentiate between factors and terms of a polynomial expression  
+
* Differentiate between factors and terms of a polynomial expression.
  
 
|-
 
|-
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||
 
||
 
Students will be able to:
 
Students will be able to:
* Solving linear equations in one variable
+
* Solve linear equations in one variable.
* Determine a linear equation
+
* Determine a linear equation.
* Write and interpret a linear equation
+
* Write and interpret a linear equation.
* Graph a linear equation
+
* Graph a linear equation.
 
|-
 
|-
 
|Week 3
 
|Week 3
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* Basic arithmetic skills  
 
* Basic arithmetic skills  
 
* Basic understanding of [[Algebraic Properties]]
 
* Basic understanding of [[Algebraic Properties]]
* Basic understanding of [[Linear Equations]] (Module 1.1)
+
* Basic understanding of [[Linear Equations]]  
 
||
 
||
 
Students will be able to:
 
Students will be able to:
 
* Solve systems of equations by graphing.
 
* Solve systems of equations by graphing.
 
* Solve systems of equations by substitution.
 
* Solve systems of equations by substitution.
* Solve systems of equations by elimination
+
* Solve systems of equations by elimination.
 
* Identify inconsistent systems of equations containing two variables.
 
* Identify inconsistent systems of equations containing two variables.
 
* Express the solution of a system of dependent equations containing two variables.
 
* Express the solution of a system of dependent equations containing two variables.
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* [[Functions]]
 
* [[Functions]]
 
||
 
||
* Basic understanding of [[Linear Equations]] (Module 0.4)
+
* Basic understanding of [[Linear Equations]]  
 
||
 
||
 
Students will be able to:
 
Students will be able to:
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* [[Function Notation]]
 
* [[Function Notation]]
 
||
 
||
* Basic understanding of [[Functions]] (Module 2.1)
+
* Basic understanding of [[Functions]]  
 
||
 
||
 
Students will be able to:
 
Students will be able to:
* Find the value of a [[Functions]]
+
* Find the value of [[Functions]].
 
* Graph the functions listed in the library of functions.
 
* Graph the functions listed in the library of functions.
 
* Determine whether a function is one-to-one.
 
* Determine whether a function is one-to-one.
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* [[Toolkit Functions]]
 
* [[Toolkit Functions]]
 
||
 
||
* Basic understanding of [[Functions]] (Module 2.1)
+
* Basic understanding of [[Functions]]
 
||
 
||
 
Students will be able to:
 
Students will be able to:
* Identify the basic toolkit functions
+
* Identify the basic toolkit functions.
* Determine [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for the basic toolkit functions (Module 2.2)
+
* Determine [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for the basic toolkit functions.
  
 
|-
 
|-
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* [[Composition of Functions]]
 
* [[Composition of Functions]]
 
||
 
||
* Basic understanding of [[Functions]] (Module 2.1)
+
* Basic understanding of [[Functions]]  
* Basic understanding of [[Function Notation]] (Module 2.2)
+
* Basic understanding of [[Function Notation]]  
* Basic understanding of [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.2)
+
* Basic understanding of [[Domain of a Function|Domain]] and [[Range of a Function| Range]]  
 
||
 
||
 
Students will be able to:
 
Students will be able to:
* Combine functions using [[Algebraic Properties]]
+
* Combine functions using [[Algebraic Properties]].
* Create a new function by composition of functions
+
* Create a new function by composition of functions.
* Evaluate composite functions
+
* Evaluate composite functions.
* Find the domain of a composite function
+
* Find the domain of a composite function.
* Decompose a composite function into its component functions
+
* Decompose a composite function into its component functions.
 
|-
 
|-
 
|Week 5
 
|Week 5
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* [[Inverse Functions]]
 
* [[Inverse Functions]]
 
||
 
||
* Basic understanding of [[Functions]] (Module 2.1)
+
* Basic understanding of [[Functions]]  
* Basic understanding of [[Function Notation]] (Module 2.2)
+
* Basic understanding of [[Function Notation]]  
* Basic understanding of [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.2)
+
* Basic understanding of [[Domain of a Function|Domain]] and [[Range of a Function| Range]]  
* Basic understanding of [[Composition of Functions]] (Module 3.1)
+
* Basic understanding of [[Composition of Functions]]
 
||
 
||
Students will be to able to:
+
Students will be able to:
* Verify inverse functions using [[Algebraic Properties]]
+
* Verify inverse functions using [[Algebraic Properties]].
* Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one
+
* Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one.
* Find or evaluate the inverse of a function
+
* Find or evaluate the inverse of a function.
* Use the graph of a one-to-one function to graph its inverse function on the same axes
+
* Use the graph of a one-to-one function to graph its inverse function on the same axes.
  
 
|-
 
|-
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* [[Exponential Functions]]
 
* [[Exponential Functions]]
 
||
 
||
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] of the [[Toolkit Functions]] for exponential functions (Module 2.2)
+
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] of the [[Toolkit Functions]] for exponential functions  
* Basic understanding of [[Exponential Properties]] (Module 4.1)
+
* Basic understanding of [[Exponential Properties]]  
 
||
 
||
 
Students will be able to:
 
Students will be able to:
* Determine the difference between [[Linear Equations|Linear]] and Exponential Functions (Module 1.1)
+
* Determine the difference between [[Linear Equations|Linear]] and Exponential Functions.
 
* Evaluate exponential functions.
 
* Evaluate exponential functions.
 
* Find the equation of an exponential function.
 
* Find the equation of an exponential function.
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* [[Logarithmic Properties]]
 
* [[Logarithmic Properties]]
 
||
 
||
* Basic understanding of [[Exponential Properties]] (Module 4.1)
+
* Basic understanding of [[Exponential Properties]]  
 
||
 
||
Students will be to able:
+
Students will be to able to:
* Rewriting from exponential form to logarithmic form and vice versa  
+
* Rewrite from exponential form to logarithmic form and vice versa.
:-y=b^x\equiv\log_b(y)=x
 
 
* Use the product rule for logarithms.
 
* Use the product rule for logarithms.
 
* Use the quotient rule for logarithms.
 
* Use the quotient rule for logarithms.
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* [[Logarithmic Functions]]
 
* [[Logarithmic Functions]]
 
||
 
||
* Basic understanding of [[Inverse Functions]] (Module 3.2)
+
* Basic understanding of [[Inverse Functions]]  
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] of [[Toolkit Functions]] for logarithmic functions. (Module 2.2)
+
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] of [[Toolkit Functions]] for logarithmic functions
* Basic understanding of [[Exponential Properties]] (Module 4.1)
+
* Basic understanding of [[Exponential Properties]]  
  
 
||
 
||
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||
 
||
 
Students will be able to:
 
Students will be able to:
* Determine complex number solutions
+
* Determine complex number solutions.
* Determine solutions of quadratic equations using factoring techniques
+
* Determine solutions of quadratic equations using factoring techniques.
* Determine solutions of quadratic equations using Quadratic Formula
+
* Determine solutions of quadratic equations using Quadratic Formula.
  
 
|-
 
|-
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||
 
||
 
Students will be able to:
 
Students will be able to:
* Basic understanding of a polynomial expression.
+
* Understand a polynomial expression.
* Recognize characteristics of parabolas
+
* Recognize characteristics of parabolas.
* Understand how the graph of a parabola is related to its quadratic function
+
* Understand how the graph of a parabola is related to its quadratic function.
* Determine a quadratic function's minimum or maximum value
+
* Determine a quadratic function's minimum or maximum value.
* Solve problems involving a quadratic function's minimum or maximum value
+
* Solve problems involving a quadratic function's minimum or maximum value.
  
  
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* [[Dividing Polynomials]]
 
* [[Dividing Polynomials]]
 
||
 
||
* Basic understanding of  [[Fractions]] (Fundamentals)
+
* Basic understanding of  [[Fractions]]  
* Basic understanding of [[Factoring]] (Fundamentals)
+
* Basic understanding of [[Factoring]]  
* The student recalls the graphs and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module  2.2)
+
* The student recalls the graphs and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| Range]]  
* Basic understanding of [[Quadratic Functions]] (Module 6.2)
+
* Basic understanding of [[Quadratic Functions]]  
  
 
||
 
||
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* Identify polynomial functions.
 
* Identify polynomial functions.
 
* Identify the degree and leading coefficients of polynomial functions.
 
* Identify the degree and leading coefficients of polynomial functions.
* Use long division to divide polynomials
+
* Use long division to divide polynomials.
* Use synthetic division to divide polynomials
+
* Use synthetic division to divide polynomials.
 
|-
 
|-
 
|Week 9
 
|Week 9
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* [[Factoring Polynomials|Zeros of Polynomials]]
 
* [[Factoring Polynomials|Zeros of Polynomials]]
 
||
 
||
* Basic understanding of  [[Fractions]] (Fundamentals)
+
* Basic understanding of  [[Fractions]]  
* Basic understanding of [[Functions]] (Module 2.1)
+
* Basic understanding of [[Functions]]  
* Basic understanding of [[Dividing Polynomials]] (Module 7.1)
+
* Basic understanding of [[Dividing Polynomials]]  
 
||
 
||
 
Students will be able to:  
 
Students will be able to:  
* Evaluate a polynomial using the Remainder Theorem
+
* Evaluate a polynomial using the Remainder Theorem.
* Use the Factor Theorem to solve a polynomial equation
+
* Use the Factor Theorem to solve a polynomial equation.
* Use the Rational Zero Theorem to find rational zeros
+
* Use the Rational Zero Theorem to find rational zeros.
* Find zeros of a polynomial function
+
* Find zeros of a polynomial function.
* Solve real-world applications of polynomial equations
+
* Solve real-world applications of polynomial equations.
  
 
|-
 
|-
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* [[Power and Polynomial Functions]]
 
* [[Power and Polynomial Functions]]
 
||
 
||
* Basic understanding of [[Factoring]] (Fundamentals)
+
* Basic understanding of [[Factoring]]  
* Basic understanding of [[Quadratic Functions]] (Module 6.2)
+
* Basic understanding of [[Quadratic Functions]]  
* Basic understanding of [[Dividing Polynomials]] (Module 7.1)
+
* Basic understanding of [[Dividing Polynomials]]  
* Basic understanding of [[Factoring Polynomials|Zeros of Polynomials]] (Module 7.2)
+
* Basic understanding of [[Factoring Polynomials|Zeros of Polynomials]]  
 
||
 
||
 
Students will be able to:  
 
Students will be able to:  
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* [[Graphs of Polynomials]]
 
* [[Graphs of Polynomials]]
 
||
 
||
* Basic understanding of [[Dividing Polynomials]] (Module 7.1)
+
* Basic understanding of [[Dividing Polynomials]]  
* Basic understanding of [[Factoring Polynomials|Zeros of Polynomials]] (Module 7.2)
+
* Basic understanding of [[Factoring Polynomials|Zeros of Polynomials]]  
 
||
 
||
 
Students will be able to:  
 
Students will be able to:  
* Recognize characteristics of graphs of polynomial functions
+
* Recognize characteristics of graphs of polynomial functions.
* Use [[Factoring]] to find zeros of polynomial functions
+
* Use [[Factoring]] to find zeros of polynomial functions.
* Identify zeros and their multiplicities
+
* Identify zeros and their multiplicities.
* Determine end behavior of polynomial functions
+
* Determine end behavior of polynomial functions.
* Understand the relationship between degree and turning points
+
* Understand the relationship between degree and turning points.
* Graph polynomial functions
+
* Graph polynomial functions.
  
 
|-
 
|-
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* [[Rational Expressions]]
 
* [[Rational Expressions]]
 
||
 
||
* The student understands that zero in the denominator of a fraction is undefined.
+
* The student understands that zero in the denominator of a fraction is undefined
* Basic understanding of  [[Fractions]] (Fundamentals)
+
* Basic understanding of  [[Fractions]]  
 
||
 
||
 
Students will be able to:
 
Students will be able to:
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* [[Graphs of Rational Functions]]
 
* [[Graphs of Rational Functions]]
 
||
 
||
* Basic understanding of [[Rational Expressions]] (Module 9.1)
+
* Basic understanding of [[Rational Expressions]]  
 
||
 
||
 
Students will be able to:  
 
Students will be able to:  
* Identify and graph vertical asymptotes
+
* Identify and graph vertical asymptotes.
* Identify and graph horizontal asymptotes
+
* Identify and graph horizontal asymptotes.
* Determine behavior of rational functions around vertical asymptotes
+
* Determine behavior of rational functions around vertical asymptotes.
* Find the domains of rational functions
+
* Find the domains of rational functions.
* Graph rational functions
+
* Graph rational functions.
  
 
|-
 
|-
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* [[Single Transformations of Functions]]
 
* [[Single Transformations of Functions]]
 
||
 
||
* Understanding of [[Function Notation]] (Module 2.1)
+
* Understanding of [[Function Notation]]  
 
||
 
||
 
Students will be able to:  
 
Students will be able to:  
* Graph functions using vertical and horizontal shifts
+
* Graph functions using vertical and horizontal shifts.
* Graph functions using reflections about the x-axis and the y-axis
+
* Graph functions using reflections about the x-axis and the y-axis.
  
 
|-
 
|-
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* [[Multiple Transformations of Functions]]
 
* [[Multiple Transformations of Functions]]
 
||
 
||
* Understanding of [[Single Transformations of Functions]] (Module 10.1)
+
* Understanding of [[Single Transformations of Functions]]  
 
||
 
||
 
Students will be able to:  
 
Students will be able to:  
* Determine whether a function is even, odd, or neither
+
* Determine whether a function is even, odd, or neither.
* Graph functions using compressions and stretches
+
* Graph functions using compressions and stretches.
* Combine transformations
+
* Combine transformations.
  
  
  
 
|}
 
|}

Latest revision as of 08:04, 23 June 2023

College Algebra for Scientists and Engineers - MAT 1073

Course Catalog

MAT 1073. Algebra for Scientists and Engineers. (1-4) 3 Credit Hours. (TCCN = MATH 1314).

Prerequisite: Satisfactory performance on a placement examination. This course is designed to prepare the student for MAT1093 Precalculus and MAT1214 Calculus I. Topics may include algebraic expressions; equations; inequalities over the real numbers; relations; functions; polynomial and rational functions; logarithmic and exponential functions; systems of linear equations and inequalities; matrices and determinants; complex numbers; sequences; series binomial expansion; mathematical induction; permutations, and combinations. (Formerly MTC 1073. Credit can be earned for only one of the following: MAT 1073, MTC 1073, MAT1063, MTC 1023, or MAT1023. NOTE: For the purpose of the Three-Attempt Rule, these courses are considered to be equivalent and additional fees may be charged for the third or subsequent attempt to take any of these courses in any combination.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: LRC1 $12; LRS1 $45; STSI $21.

Topics List

Week Sections Topics Prerequisite Skills Student Learning Outcomes
Week 1

Fundamentals

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills

Students will be able to correctly identify the algebraic properties:

  • Additive & Multiplicative identity
  • Additive & Multiplicative inverse
  • Commutative property
  • Associative property
  • Distributive property


Students will be able to correctly explain the algebraic properties of numbers and correctly apply these properties in procedural explanations of:

  • Solving mathematical equations
  • Simplifying/evaluating mathematical expressions
Week 2

Fundamentals

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of Algebraic Properties


Students will be able to:

  • Add and subtract fractions.
  • Determine common denominators and equivalent fractions.
  • Work with proper and improper fractions.
  • Simplify to lowest terms.
  • Multiply and divide fractions.
Week 2

Fundamentals

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of Algebraic Properties


Students will be able to:

  • Identify factored vs non-factored forms of a polynomial.
  • Successfully factor binomials & trinomials and difference of squares into two binomial terms.
  • Factor out GCF.
  • Multiply and/or distribute to check their factors are correct.
  • Differentiate between factors and terms of a polynomial expression.
Week 3

Module 1.1

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of Algebraic Properties
  • Understanding of the Cartesian coordinate system

Students will be able to:

  • Solve linear equations in one variable.
  • Determine a linear equation.
  • Write and interpret a linear equation.
  • Graph a linear equation.
Week 3

Module 1.2

Students will be able to:

  • Solve systems of equations by graphing.
  • Solve systems of equations by substitution.
  • Solve systems of equations by elimination.
  • Identify inconsistent systems of equations containing two variables.
  • Express the solution of a system of dependent equations containing two variables.
Week 4

Module 2.1

Students will be able to:

  • Determine whether a relation represents a function.
Week 4

Module 2.2

Students will be able to:

  • Find the value of Functions.
  • Graph the functions listed in the library of functions.
  • Determine whether a function is one-to-one.
  • Use the vertical line test to identify functions.
Week 4

Module 2.2

Students will be able to:

  • Find the domain of a function defined by an equation.
Week 4

Module 2.2

Students will be able to:

  • Find the range of a function defined by an equation.
Week 4

Module 2.2

Students will be able to:

  • Identify the basic toolkit functions.
  • Determine Domain and Range for the basic toolkit functions.
Week 5

Module 3.1

Students will be able to:

  • Combine functions using Algebraic Properties.
  • Create a new function by composition of functions.
  • Evaluate composite functions.
  • Find the domain of a composite function.
  • Decompose a composite function into its component functions.
Week 5

Module 3.2

Students will be able to:

  • Verify inverse functions using Algebraic Properties.
  • Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one.
  • Find or evaluate the inverse of a function.
  • Use the graph of a one-to-one function to graph its inverse function on the same axes.
Week 6

Module 4.1

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of Algebraic Properties

Students will be able to:

  • Use the product rule for exponents.
  • Use the quotient rule for exponents.
  • Use the power rule for exponents.
Week 6

Module 4.2

Students will be able to:

  • Determine the difference between Linear and Exponential Functions.
  • Evaluate exponential functions.
  • Find the equation of an exponential function.
  • Evaluate exponential functions with base e.
  • Evaluate exponential functions with base 10.
  • Graph exponential functions.
Week 7

Module 5.1

Students will be to able to:

  • Rewrite from exponential form to logarithmic form and vice versa.
  • Use the product rule for logarithms.
  • Use the quotient rule for logarithms.
  • Use the power rule for logarithms.
  • Expand logarithmic expressions.
  • Condense logarithmic expressions.
  • Use the change-of-base formula for logarithms.
Week 7

Module 5.2

Students will be able to:

  • Evaluate logarithms.
  • Use common logarithms.
  • Use natural logarithms.
  • Graph logarithmic functions.
Week 8

Module 6.2

Students will be able to:

  • Determine complex number solutions.
  • Determine solutions of quadratic equations using factoring techniques.
  • Determine solutions of quadratic equations using Quadratic Formula.
Week 8

Module 6.2

Students will be able to:

  • Understand a polynomial expression.
  • Recognize characteristics of parabolas.
  • Understand how the graph of a parabola is related to its quadratic function.
  • Determine a quadratic function's minimum or maximum value.
  • Solve problems involving a quadratic function's minimum or maximum value.


Week 9

Module 7.1

Students will be able to:

  • Identify polynomial functions.
  • Identify the degree and leading coefficients of polynomial functions.
  • Use long division to divide polynomials.
  • Use synthetic division to divide polynomials.
Week 9

Module 7.2

Students will be able to:

  • Evaluate a polynomial using the Remainder Theorem.
  • Use the Factor Theorem to solve a polynomial equation.
  • Use the Rational Zero Theorem to find rational zeros.
  • Find zeros of a polynomial function.
  • Solve real-world applications of polynomial equations.
Week 10

Module 8.1

Students will be able to:

  • Find the average rate of change of a function.
  • Use a graph to determine where a function is increasing, decreasing, or constant.
  • Use a graph to locate local maxima and local minima.
  • Use a graph to locate the absolute maximum and absolute minimum.
  • Identify end behavior of power functions.


Week 10

Module 8.2

Students will be able to:

  • Recognize characteristics of graphs of polynomial functions.
  • Use Factoring to find zeros of polynomial functions.
  • Identify zeros and their multiplicities.
  • Determine end behavior of polynomial functions.
  • Understand the relationship between degree and turning points.
  • Graph polynomial functions.
Week 11

Module 9.1

  • The student understands that zero in the denominator of a fraction is undefined
  • Basic understanding of Fractions

Students will be able to:

  • Simplify rational expressions.
  • Multiply rational expressions.
  • Divide rational expressions.
  • Add and subtract rational expressions.
Week 11

Module 9.2

Students will be able to:

  • Identify and graph vertical asymptotes.
  • Identify and graph horizontal asymptotes.
  • Determine behavior of rational functions around vertical asymptotes.
  • Find the domains of rational functions.
  • Graph rational functions.
Week 12

Module 10.1

Students will be able to:

  • Graph functions using vertical and horizontal shifts.
  • Graph functions using reflections about the x-axis and the y-axis.
Week 12

Module 10.2

Students will be able to:

  • Determine whether a function is even, odd, or neither.
  • Graph functions using compressions and stretches.
  • Combine transformations.