Rational functions THURSDAY 11/21

Front

What are x-intercepts?

Back

The x-intercepts of a function are the points where the graph of the function crosses the x-axis. This occurs when the output (y-value) is zero.

Front

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

Back

To find the y-intercept, plug 0 in for all x-values in the function.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where the function approaches infinity or negative infinity as x approaches a.

Front

How do you determine vertical asymptotes in a rational function?

Back

Vertical asymptotes occur at the values of x that make the denominator equal to zero, provided those values do not also make the numerator zero.

Front

What is a horizontal asymptote?

Back

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

Front

How do you find horizontal asymptotes in rational functions?

Back

To find horizontal asymptotes, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the denominator, y = 0 is the horizontal asymptote.

Front

What does it mean if a rational function has no horizontal asymptote?

Back

If the degree of the numerator is greater than the degree of the denominator, the function does not have a horizontal asymptote.

Front

What is the significance of the factors in the numerator of a rational function?

Back

The factors in the numerator determine the x-intercepts of the function.

Front

What is the significance of the factors in the denominator of a rational function?

Back

The factors in the denominator determine the vertical asymptotes and points of discontinuity of the function.

Front

How do you graph a rational function?

Back

To graph a rational function, identify x-intercepts, y-intercepts, vertical asymptotes, horizontal asymptotes, and plot points to understand the behavior of the function.