Toolkit Functions - Revision history

Lila: /* Resources */

2021-10-21T18:52:49Z

Resources

Lila at 19:32, 4 October 2021

2021-10-04T19:32:45Z

Lila at 19:24, 4 October 2021

2021-10-04T19:24:41Z

Lila at 19:23, 4 October 2021

2021-10-04T19:23:19Z

Lila at 19:15, 4 October 2021

2021-10-04T19:15:13Z

Lila: /* Constant Function */

2021-10-04T18:59:40Z

Constant Function

Lila at 18:47, 4 October 2021

2021-10-04T18:47:23Z

Lila at 18:46, 4 October 2021

2021-10-04T18:46:02Z

Lila at 18:45, 4 October 2021

2021-10-04T18:45:38Z

Lila: /* Resources */

2021-10-04T18:45:20Z

Resources

← Older revision		Revision as of 18:52, 21 October 2021
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	* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Domain_Range_and_Toolkit_Functions/MAT1053_M1.2Domain_Range_and_Toolkit_FunctionsGN.pdf Guided Notes]		* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Domain_Range_and_Toolkit_Functions/MAT1053_M1.2Domain_Range_and_Toolkit_FunctionsGN.pdf Guided Notes]
	* [https://courses.lumenlearning.com/cuny-hunter-collegealgebra/chapter/toolkit-functions/ Toolkit Functions], Lumen Learning		* [https://courses.lumenlearning.com/cuny-hunter-collegealgebra/chapter/toolkit-functions/ Toolkit Functions], Lumen Learning
		+
		+	== Licensing ==
		+	Content obtained and/or adapted from:
		+	* [https://courses.lumenlearning.com/cuny-hunter-collegealgebra/chapter/toolkit-functions/ Toolkit Functions, Lumen Learning: Hunter College MATH101] under a CC0 (public domain) license

@@ Line 1: / Line 1: @@
 ===Constant Function===
-[[File:Constant function.png|thumb|Constant function]]
+[[File:Constant function.png|thumb|left|Constant function]]
 For the constant function
 <math> f(x) = c </math>
@@ Line 8: / Line 13: @@
 Range: <math>[c, c]</math>
@@ Line 14: / Line 21: @@
 ===Identity Function===
 [[File:Identity function.png|thumb|left|Identity function]]
 For the identity function
 <math> f(x) = x </math>
@@ Line 21: / Line 34: @@
 Range: <math> ( -\infty ,\infty ) </math>
@@ Line 26: / Line 41: @@
 ===Absolute Value Function===
-[[File:Absolute value function.png|thumb|Absolute value function]]
+[[File:Absolute value function.png|thumb|left|Absolute value function]]
 For the absolute value function
 <math> f(x) = |x| </math>
@@ Line 34: / Line 54: @@
 Range : <math> [0 ,\infty ) </math>
@@ Line 40: / Line 62: @@
 ===Quadratic Function===
 [[File:Quadratic toolkit function.png|thumb|left|Quadratic function]]
 For the quadratic function
 <math> f(x) = x^2 </math>
@@ Line 47: / Line 74: @@
 Range : <math> [0 ,\infty ) </math>
@@ Line 52: / Line 81: @@
 ===Cubic Function===
-[[File:Cubic toolkit function.png|thumb|Cubic function]]
+[[File:Cubic toolkit function.png|thumb|left|Cubic function]]
 For the cubic function
 <math> f(x) = x^3 </math>
@@ Line 60: / Line 94: @@
 Range: <math> ( -\infty ,\infty ) </math>
@@ Line 65: / Line 101: @@
 ===Rational Function===
-[[File:Rational function.png|thumb|Rational function]]
+[[File:Rational function.png|thumb|left|Rational function]]
 For the rational function (also known as the reciprocal function)
 <math>  f(x) = \frac{1}{x} </math>
@@ Line 73: / Line 114: @@
 Range: <math> ( -\infty , 0) \cup (0, \infty ) </math>
@@ Line 78: / Line 121: @@
 ===Squared Rational Function===
-[[File:Squared rational function.png|thumb|Squared rational function]]
+[[File:Squared rational function.png|thumb|left|Squared rational function]]
 For the squared rational function
 <math>  f(x) = \frac{1}{x^2} </math>
@@ Line 86: / Line 134: @@
 Range: <math> (0, \infty ) </math>
@@ Line 91: / Line 141: @@
 ===Square Root Function===
-[[File:Square root function.png|thumb|Square root function]]
+[[File:Square root function.png|thumb|left|Square root function]]
 For the square root function
 <math> f(x) = \sqrt{x} </math>
@@ Line 99: / Line 154: @@
 Range: <math> [0, \infty ) </math>
@@ Line 104: / Line 161: @@
 ===Cube Root Function===
-[[File:Cube root function.png|thumb|Cube root function]]
+[[File:Cube root function.png|thumb|left|Cube root function]]
 For the cube root function
 <math> f(x) = \sqrt[3]{x} </math>
@@ Line 112: / Line 174: @@
 Range: <math> ( -\infty ,\infty ) </math>

@@ Line 13: / Line 13: @@
 ===Identity Function===
-[[File:Identity function.png|thumb|Identity function]]
+[[File:Identity function.png|thumb|left|Identity function]]
 For the identity function
 <math> f(x) = x </math>
@@ Line 39: / Line 39: @@
 ===Quadratic Function===
-[[File:Quadratic toolkit function.png|thumb|Quadratic function]]
+[[File:Quadratic toolkit function.png|thumb|left|Quadratic function]]
 For the quadratic function
 <math> f(x) = x^2 </math>

@@ Line 1: / Line 1: @@
 ===Constant Function===
 For the constant function
 <math> f(x) = c </math>
@@ Line 7: / Line 8: @@
 Range: <math>[c, c]</math>
 ===Identity Function===
 For the identity function
 <math> f(x) = x </math>
@@ Line 16: / Line 21: @@
 Range: <math> ( -\infty ,\infty ) </math>
 ===Absolute Value Function===
 For the absolute value function
 <math> f(x) = |x| </math>
@@ Line 25: / Line 34: @@
 Range : <math> [0 ,\infty ) </math>
 ===Quadratic Function===
 For the quadratic function
 <math> f(x) = x^2 </math>
@@ Line 34: / Line 47: @@
 Range : <math> [0 ,\infty ) </math>
 ===Cubic Function===
 For the cubic function
 <math> f(x) = x^3 </math>
@@ Line 43: / Line 60: @@
 Range: <math> ( -\infty ,\infty ) </math>
 ===Rational Function===
 For the rational function (also known as the reciprocal function)
 <math>  f(x) = \frac{1}{x} </math>
@@ Line 52: / Line 73: @@
 Range: <math> ( -\infty , 0) \cup (0, \infty ) </math>
 ===Squared Rational Function===
 For the squared rational function
 <math>  f(x) = \frac{1}{x^2} </math>
@@ Line 61: / Line 86: @@
 Range: <math> (0, \infty ) </math>
 ===Square Root Function===
 For the square root function
 <math> f(x) = \sqrt{x} </math>
@@ Line 70: / Line 99: @@
 Range: <math> [0, \infty ) </math>
 ===Cube Root Function===
 For the cube root function
 <math> f(x) = \sqrt[3]{x} </math>
@@ Line 79: / Line 112: @@
 Range: <math> ( -\infty ,\infty ) </math>
 ==Resources==

@@ Line 45: / Line 45: @@
 ===Rational Function===
-For the reciprocal function
+For the rational function (also known as the reciprocal function)
 <math>  f(x) = \frac{1}{x} </math>
 we cannot divide by 0, so we must exclude 0 from the domain. Further, 1 divided by any value can never be 0, so the range also will not include 0.
@@ Line 52: / Line 52: @@
 Range: <math> ( -\infty , 0) \cup (0, \infty ) </math>
 ==Resources==

← Older revision		Revision as of 18:59, 4 October 2021
Line 7:		Line 7:

	Range: <math>[c, c]</math>		Range: <math>[c, c]</math>
		+
		+	===Identity Function===
		+	For the identity function
		+	<math> f(x) = x </math>
		+	there is no restriction on <math> x </math>. Both the domain and range are the set of all real numbers.
		+
		+	Domain: <math> ( -\infty ,\infty ) </math>
		+
		+	Range: <math> ( -\infty ,\infty ) </math>
		+
		+	===Absolute Value Function===
		+	For the absolute value function
		+	<math> f(x) = \|x\| </math>
		+	there is no restriction on x. The outputs are <math> x </math> for <math> x\ge 0 </math> and <math> -x </math> for <math> x < 0 </math>, so the range is all numbers greater than or equal to 0.
		+
		+	Domain: <math> ( -\infty ,\infty ) </math>
		+
		+	Range : <math> [0 ,\infty ) </math>
		+
		+	===Quadratic Function===
		+	For the quadratic function
		+	<math> f(x) = x^2 </math>
		+	the domain is all real numbers since the horizontal extent of the graph is the whole real number line. Because the graph does not include any negative values for the range, the range is only nonnegative real numbers.
		+
		+	Domain: <math> ( -\infty ,\infty ) </math>
		+
		+	Range : <math> [0 ,\infty ) </math>
		+
		+	===Cubic Function===
		+	For the cubic function
		+	<math> f(x) = x^3 </math>
		+	the domain is all real numbers because the horizontal extent of the graph is the whole real number line. The same applies to the vertical extent of the graph, so the domain and range include all real numbers.
		+
		+	Domain: <math> ( -\infty ,\infty ) </math>
		+
		+	Range: <math> ( -\infty ,\infty ) </math>
		+
		+	===Rational Function===
		+	For the reciprocal function
		+	<math> f(x) = \frac{1}{x} </math>
		+	we cannot divide by 0, so we must exclude 0 from the domain. Further, 1 divided by any value can never be 0, so the range also will not include 0.
		+
		+	Domain: <math> ( -\infty , 0) \cup (0, \infty ) </math>
		+
		+	Range: <math> ( -\infty , 0) \cup (0, \infty ) </math>

	==Resources==		==Resources==

@@ Line 3: / Line 3: @@
 <math> f(x) = c </math>
 the domain consists of all real numbers; there are no restrictions on the input. The only output value is the constant <math> c </math>, so the range is the set <math>\{c\}</math> that contains this single element. In interval notation, this is written as <math>[c,c]</math>, the interval that both begins and ends with <math>c</math>.
-Domain: <math> \( -\infty,\infty\) </math>
-Range: [c, c]
+Domain: <math> ( -\infty ,\infty ) </math>
 ==Resources==