Exploring Rational Function Graphs

Front

What is a rational function?

Back

Front

What is a horizontal asymptote?

Back

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

Front

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

Back

Front

What is the y-intercept of a function?

Back

The y-intercept of a function is the value of the function when x = 0, found by evaluating f(0).

Front

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

Back

Front

What is end behavior in the context of rational functions?

Back

End behavior describes how the values of a function behave as x approaches positive or negative infinity.

Front

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

Back

To analyze the end behavior of a rational function, determine the degrees of the numerator and denominator and use the leading coefficients to find the horizontal asymptote.

Front

What is the significance of the leading coefficient in a rational function?

Back

The leading coefficient of the highest degree term in the numerator and denominator helps determine the horizontal asymptote and the end behavior of the function.

Front

What happens to the graph of a rational function at vertical asymptotes?

Back

At vertical asymptotes, the function approaches infinity or negative infinity, and the graph will not cross these lines.

Front

How do you find vertical asymptotes of a rational function?

Back

Vertical asymptotes occur where the denominator of the rational function equals zero, provided the numerator does not also equal zero at those points.