Section 7.2: Graph Simple Rational Functions

Section 7.2: Graph Simple Rational Functions

9th - 12th Grade

15 Qs

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Section 7.2: Graph Simple Rational Functions

Section 7.2: Graph Simple Rational Functions

Assessment

Quiz

Mathematics

9th - 12th Grade

Practice Problem

Easy

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15 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the significance of the degrees of the numerator and denominator in determining horizontal asymptotes?

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0.

If the degree of the numerator is greater than the degree of the denominator, the horizontal asymptote is y = infinity.

If the degrees of the numerator and denominator are equal, the horizontal asymptote is y = leading coefficient of numerator / leading coefficient of denominator.

The horizontal asymptote is always y = 1 regardless of the degrees.

2.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

How do you determine the x-intercepts of a rational function?

By setting the denominator equal to zero and solving for x.

By setting the numerator equal to zero and solving for x.

By finding the vertex of the function.

By evaluating the function at x = 0.

3.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the general form of a rational function?

f(x) = P(x) + Q(x), where P(x) and Q(x) are polynomials.

f(x) = P(x) * Q(x), where P(x) and Q(x) are polynomials.

f(x) = P(x)/Q(x), where P(x) and Q(x) are polynomials.

f(x) = P(x) - Q(x), where P(x) and Q(x) are polynomials.

4.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the horizontal asymptote of a rational function?

A horizontal line that the graph approaches as x approaches infinity or negative infinity.

A vertical line that the graph approaches as x approaches infinity.

The point where the graph intersects the x-axis.

The maximum value of the function as x approaches infinity.

5.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What are the steps to graph a rational function?

1. Identify vertical and horizontal asymptotes, determine intercepts, analyze behavior around asymptotes, and plot additional points.

2. Find the roots of the function, calculate the derivative, and plot the function's critical points.

3. Simplify the function, find the domain, and plot the function on a graphing calculator.

4. Identify the function type, calculate the area under the curve, and sketch the graph.

6.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is a rational function?

A function that can be expressed as the ratio of two polynomials.

A function that is always increasing or decreasing.

A function that has a constant value for all inputs.

A function that can only be defined for integer values.

7.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

How do you find vertical asymptotes in a rational function?

Set the numerator of the rational function equal to zero and solve for x.

Set the denominator of the rational function equal to zero and solve for x.

Find the limits of the function as x approaches infinity.

Differentiate the function and find critical points.

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