Question

List the critical points/features that should be found before graphing a function.

Accepted Answer

**y-intercept**, found by setting input variable equal to 0 and solving for the output variable, usually *y*.   
**x-intercept(s)**, or **roots**, found by setting the output equal to 0 and solving for input variable, usually *x*.

The **domain** is the collection of input values for which the function is defined. A function’s domain is undefined for values that lead to division by 0 or values that yield imaginary results, as in the case of negative values within a radical.

The **range** is the collection of output values produced by the domain. The range will not be defined at particular horizontal asymptotes, which arise in rational functions that have a numerator and a denominator of the same degree, $$\frac{x^2}{2x^2}$$ for example, or in the case where the degree of the numerator is smaller than the degree of the denominator, $$\frac{x}{x^2}$$ for example. 

**End behavior** is how the function behaves as the input values become very large or very small. In addition to this end behavior, it is also useful to determine the function’s **behavior on either side of vertical asymptotes**.

Flashcard 5 - Next Generation Advanced Algebra and Functions Flashcard Set for the ACCUPLACER Test

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