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

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.

Many functions will not be easily factorable or manageable. In such cases, it is incredibly useful to build a collection of critical points and features that can help pinpoint specific input values that can be evaluated which will help to produce the graph.