Math 3 Unit 4 Lesson 1 Review

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What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a rational function approaches infinity or negative infinity as x approaches a. It occurs where the denominator of the function is zero and the numerator is not zero.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b that a function approaches as x approaches infinity or negative infinity. It indicates the behavior of the function at extreme values of x.

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

Back

To find the x-intercept of a function, set the function equal to zero and solve for x. The x-intercept is the point where the graph crosses the x-axis.

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

Back

To find the y-intercept of a function, evaluate the function at x = 0. The y-intercept is the point where the graph crosses the y-axis.

Front

What is the domain of a rational function?

Back

The domain of a rational function is all real numbers except where the denominator is zero. It is expressed in interval notation.

Front

What is the significance of the x-intercept in a rational function?

Back

The x-intercept indicates the value of x where the function equals zero. It shows where the graph crosses the x-axis.

Front

What is the significance of the y-intercept in a rational function?

Back

The y-intercept indicates the value of the function when x = 0. It shows where the graph crosses the y-axis.

Front

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

Back

To determine the horizontal asymptote, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the denominator, y = 0; if they are equal, y = leading coefficient of numerator/leading coefficient of denominator.

Front

What is the general form of a rational function?

Back

Front

What does it mean if a rational function has a vertical asymptote at x = a?

Back

It means that as x approaches a, the function's value approaches infinity or negative infinity, indicating a discontinuity at that point.