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.

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

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.

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.

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.

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.

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.