Pre-Calc P5 HW:12.05.24: Graphs of Rational Functions

Front

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

Back

Make the numerator equal to 0.

Front

Back

x = -1 and x = 5.

Front

Back

x = -3 and x = 7.

Front

How is the Horizontal Asymptote determined?

Back

By comparing the degrees of the numerator and denominator.

Front

What does it mean if the degrees of the numerator and denominator are equal?

Back

The horizontal asymptote is found by dividing the leading coefficients.

Front

What is the significance of vertical asymptotes in rational functions?

Back

They indicate values of x where the function approaches infinity or negative infinity.

Front

How do you determine the end behavior of a rational function?

Back

By analyzing the degrees of the numerator and denominator.

Front

What happens to the graph of a rational function at its x-intercepts?

Back

The graph crosses the x-axis.

Front

What is the relationship between the degree of the numerator and the degree of the denominator for horizontal asymptotes?

Back

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0.

Front

What is a rational function?

Back

A function that can be expressed as the ratio of two polynomials.