Difference between revisions of "Toolkit Functions"

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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
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== Licensing ==
 +
Content obtained and/or adapted from:
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* [https://courses.lumenlearning.com/cuny-hunter-collegealgebra/chapter/toolkit-functions/ Toolkit Functions, Lumen Learning: Hunter College MATH101] under a CC0 (public domain) license

Latest revision as of 12:52, 21 October 2021

Constant Function

Constant function



For the constant function the domain consists of all real numbers; there are no restrictions on the input. The only output value is the constant , so the range is the set that contains this single element. In interval notation, this is written as , the interval that both begins and ends with .

Domain:

Range:




Identity Function

Identity function




For the identity function there is no restriction on . Both the domain and range are the set of all real numbers.

Domain:

Range:




Absolute Value Function

Absolute value function



For the absolute value function there is no restriction on x. The outputs are for and for , so the range is all numbers greater than or equal to 0.

Domain:

Range :




Quadratic Function

Quadratic function



For the quadratic function 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:

Range :




Cubic Function

Cubic function



For the cubic function 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:

Range:




Rational Function

Rational function



For the rational function (also known as the reciprocal function) 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:

Range:




Squared Rational Function

Squared rational function



For the squared rational function 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. Also, since for all , the range will only consist of positive numbers.

Domain:

Range:




Square Root Function

Square root function



For the square root function we cannot take the square root of a negative real number, so the domain must be 0 or greater. The range also excludes negative numbers because the square root of a positive number is defined to be positive, even though the square of the negative number also gives us .

Domain:

Range:




Cube Root Function

Cube root function



For the cube root function the domain and range include all real numbers. Note that there is no problem taking a cube root, or any odd-integer root, of a negative number, and the resulting output is negative (it is an odd function).

Domain:

Range:




Resources

Licensing

Content obtained and/or adapted from: