Graphing Rational Functions

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D

Front

What is a horizontal asymptote?

Back

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

Tags

CCSS.HSF-IF.C.7D

Front

How do you find vertical asymptotes of a rational function?

Back

Vertical asymptotes can be found by setting the denominator of the rational function equal to zero and solving for x.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find horizontal asymptotes of a rational function?

Back

Horizontal asymptotes can be determined by comparing the degrees of the numerator and denominator polynomials.

Tags

CCSS.HSF-IF.C.7D

Front

What does it mean for a function to be vertically stretched?

Back

A function is vertically stretched when its output values are multiplied by a factor greater than 1, making the graph taller.

Front

What is the effect of shifting a graph to the right?

Back

Shifting a graph to the right means adding a positive value to the x-variable, which moves the entire graph horizontally.

Front

What is the effect of shifting a graph down?

Back

Shifting a graph down means subtracting a value from the y-variable, which moves the entire graph vertically.

Front

What is the significance of the point where a vertical asymptote occurs?

Back

At a vertical asymptote, the function is undefined, and the graph will approach infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

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

Back

The end behavior can be determined by analyzing the leading coefficients and degrees of the numerator and denominator.

Tags

CCSS.HSF-IF.C.7D