12/10 Graphing Rational Functions Check

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a rational function approaches infinity or negative infinity as the input approaches a. It indicates values that the function cannot take.

Front

How do you find vertical asymptotes in a rational function?

Back

To find vertical asymptotes, set the denominator of the rational function equal to zero and solve for x. The solutions are the x-values where vertical asymptotes occur.

Front

What is a hole in a rational function?

Back

A hole occurs in a rational function at a point where both the numerator and denominator are zero, indicating that the function is undefined at that point but can be simplified.

Front

How do you identify holes in a rational function?

Back

To identify holes, factor both the numerator and denominator. If a common factor exists, the x-value that makes this factor zero is where the hole occurs.

Front

What is the significance of horizontal asymptotes?

Back

Horizontal asymptotes indicate the behavior of a rational function as x approaches infinity or negative infinity. They help determine the end behavior of the graph.

Front

How do you find horizontal asymptotes in a rational function?

Back

To find horizontal asymptotes, compare the degrees of the numerator and denominator. If the degree of the numerator is less, y = 0; if equal, y = leading coefficient ratio; if greater, no horizontal asymptote.

Front

What is the domain of a rational function?

Back

The domain of a rational function consists of all real numbers except those that make the denominator zero.

Front

How do you determine the range of a rational function?

Back

The range can be determined by analyzing the function's behavior, including asymptotes and holes, and identifying all possible output values.

Front

What is the x-intercept of a rational function?

Back

The x-intercept is the point where the graph crosses the x-axis, found by setting the numerator equal to zero and solving for x.

Front

What is the y-intercept of a rational function?

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating the function at x = 0.