Characteristics of Rational Functions - Exit ticket

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.

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What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches or crosses.

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.

Front

How do you determine the horizontal asymptote of a rational function?

Back

The horizontal asymptote can be determined by comparing the degrees of the numerator and denominator polynomials.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line that the graph of a function approaches as the input approaches a certain value, typically where the function is undefined.

Front

How do you find the vertical asymptote of a rational function?

Back

The vertical asymptote can be found by setting the denominator equal to zero and solving for x.

Front

What is a hole in a rational function?

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A hole occurs in a rational function at a point where both the numerator and denominator are zero, indicating a removable discontinuity.

Front

How do you find the coordinates of a hole in a rational function?

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To find the coordinates of a hole, factor the numerator and denominator, cancel the common factors, and evaluate the function at the x-value of the hole.

Front

What is the y-intercept of a function?

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

Front

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

Back

To find the y-intercept, substitute x = 0 into the function and simplify.