PREC SE 1 Review Intercepts, Asymptotes, Holes

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as the input approaches a. It indicates values that the function cannot take.

Front

How do you find the vertical asymptote of a rational function?

Back

Set the denominator equal to zero and solve for x. The values of x that make the denominator zero are the vertical asymptotes.

Front

What is an x-intercept?

Back

An x-intercept is a point where the graph of a function crosses the x-axis. At this point, the y-value is zero.

Front

How do you find the x-intercept of a function?

Back

Replace the y-value with 0 or make the numerator equal to 0.

Front

What is a y-intercept?

Back

A y-intercept is a point where the graph of a function crosses the y-axis. At this point, the x-value is zero.

Front

How do you find the y-intercept of a function?

Back

Replace all x-values with 0.

Front

What are horizontal asymptotes?

Back

Horizontal asymptotes are lines y = b that the graph of a function approaches as x approaches infinity or negative infinity.

Front

How do you find horizontal asymptotes for rational functions?

Back

Compare the degrees of the numerator and denominator. If the degree of the numerator is less, y = 0; if equal, y = leading coefficient of numerator/leading coefficient of denominator; if greater, no horizontal asymptote.

Front

What is a hole in a graph?

Back

A hole occurs in the graph of a function at a point where both the numerator and denominator are zero, indicating that the function is undefined at that point.

Front

How do you find holes in a rational function?

Back

Factor both the numerator and denominator, then identify common factors. The x-values that make these common factors zero are the locations of the holes.