Rational Functions Test Review

Front

What is a Horizontal Asymptote (H.A.)?

Back

A Horizontal Asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Front

When the degree of the numerator is greater than the degree of the denominator, what is the H.A.?

Back

none

Front

What is the first step to analyze a rational function?

Back

Factor it all out.

Front

How do you determine the Horizontal Asymptote of a rational function?

Back

Compare the degrees of the numerator and denominator.

Front

When the degree of the numerator is equal to the degree of the denominator, what is the H.A.?

Back

y = a / b, where a and b are the leading coefficients of the numerator and denominator respectively.

Front

How can you identify if a factor in the denominator is a hole instead of a vertical asymptote (V.A.)?

Back

It cancels out with a factor in the numerator.

Front

What is a Vertical Asymptote (V.A.)?

Back

A Vertical Asymptote is a vertical line x = k where the function approaches infinity or negative infinity.

Front

What happens to the graph of a rational function at a hole?

Back

The graph is not defined at that point, and it appears as a gap in the graph.

Front

What is the significance of finding x-intercepts in a rational function?

Back

X-intercepts indicate where the function crosses the x-axis, found by setting the numerator equal to zero.

Front

What is the significance of finding y-intercepts in a rational function?

Back

Y-intercepts indicate where the function crosses the y-axis, found by evaluating the function at x = 0.