Rational Functions Quiz

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Questions and Answers

What is an asymptote of a rational function?

A point where the function is undefined
The x-intercept of the function
The y-intercept of the function
A line that the graph approaches but does not touch (correct)

What does finding the zeroes of a rational function involve?

Identifying the points where the function intersects the x-axis
Solving for the values of the variable that make the function equal to zero (correct)
Calculating the slope of the function at critical points
Determining the end behavior of the function

What is the relationship between intercepts and zeroes of a rational function?

The x-intercepts are the asymptotes of the function
The y-intercepts are the asymptotes of the function
The y-intercepts are the zeroes of the function
The x-intercepts are the zeroes of the function (correct)

What is the relationship between the intercepts and zeroes of a rational function?

Intercepts are the points where the graph crosses the x-axis, and zeroes are the values of x that make the function equal to zero. (A) Signup and view all the answers

What does finding the asymptotes of a rational function involve?

Identifying the values of x for which the function approaches positive or negative infinity. (C) Signup and view all the answers

What is an asymptote of a rational function?

A line that the graph of the function approaches but does not touch as x approaches positive or negative infinity. (B) Signup and view all the answers

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Study Notes

Asymptotes of a Rational Function

An asymptote of a rational function is a line that the graph approaches as the input (x) increases or decreases without bound, but never reaches.
Finding the asymptotes of a rational function involves determining the values of x that make the denominator equal to zero.

Zeroes of a Rational Function

Finding the zeroes of a rational function involves setting the numerator equal to zero and solving for x.
The zeroes of a rational function are the values of x that make the function equal to zero.

Relationship between Intercepts and Zeroes

The x-intercepts of a rational function are the same as the zeroes of the function.
The y-intercept of a rational function is the value of the function when x is equal to zero.
The intercepts and zeroes of a rational function are related in that they are the points at which the graph of the function crosses the x-axis or y-axis.