Rational Functions Transformations and Characteristics

Front

What are the x-intercepts of the function?

Back

The x-intercepts are the points where the graph crosses the x-axis. For the given function, the x-intercepts are x = 4 and x = -2.

Tags

CCSS.HSF-IF.C.7A

Front

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

Back

To find the x-intercept, replace the y-value with 0 or make the numerator equal to 0.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D

Front

What is the horizontal asymptote of the function if the degrees of the numerator and denominator are equal?

Back

If the degrees of the numerator and denominator are equal, the horizontal asymptote is given by the ratio of the leading coefficients.

Tags

CCSS.HSF-IF.C.7D

Front

What is the horizontal asymptote of the function if the degree of the numerator is less than the degree of the denominator?

Back

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

Tags

CCSS.HSF-IF.C.7D

Front

What is the horizontal asymptote of the function if the degree of the numerator is greater than the degree of the denominator?

Back

If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

Tags

CCSS.HSF-IF.C.7D

Front

Back

In the function, 'a' represents the vertical stretch or compression factor.

Tags

CCSS.HSF-IF.C.7D

Front

Back

In the function, 'h' represents the horizontal shift of the graph.

Tags

CCSS.HSF-IF.C.7D

Front

Back

In the function, 'k' represents the vertical shift of the graph.

Tags

CCSS.HSF-IF.C.7D

Front

Back

The range of the function is all real numbers except y = 2.