Graph a rational function with vertical and oblique asymptotes

Graph a rational function with vertical and oblique asymptotes

Assessment

Interactive Video

Mathematics

11th Grade - University

Hard

Created by

Quizizz Content

FREE Resource

The video tutorial covers the process of graphing rational functions with a focus on identifying and graphing vertical, horizontal, and slant asymptotes. It begins with an introduction to vertical asymptotes, followed by a discussion on horizontal and slant asymptotes. The instructor demonstrates how to use long division to find slant asymptotes and graph them. The tutorial also includes finding X and Y intercepts and discusses the behavior of the graph concerning multiplicity of roots. The session concludes with final graphing steps and a summary of the key points.

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10 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in finding a vertical asymptote?

Set the numerator equal to zero.

Set the denominator equal to zero.

Use synthetic division.

Find the degree of the polynomial.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When is there no horizontal asymptote?

When the degree of the numerator is equal to the denominator.

When the polynomial is linear.

When the degree of the numerator is less than the denominator.

When the degree of the numerator is greater than the denominator.

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is a requirement for using synthetic division?

The divisor must be a linear binomial.

The dividend must be a quadratic polynomial.

The dividend must be a linear polynomial.

The divisor must be a quadratic binomial.

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the purpose of long division in finding slant asymptotes?

To find the remainder of the division.

To determine the degree of the polynomial.

To find the equation of the slant asymptote.

To simplify the polynomial.

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of dividing a polynomial by a linear binomial?

A quadratic polynomial.

A slant asymptote.

A linear polynomial.

A constant.

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

Use synthetic division.

Set Y to zero and solve for X.

Set X to zero and solve for Y.

Find the degree of the polynomial.

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you determine the X-intercept of a function?

Set Y to zero and solve for X.

Set X to zero and solve for Y.

Find the degree of the polynomial.

Use long division.

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