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Understanding Limits of Rational Functions

Understanding Limits of Rational Functions

Assessment

Interactive Video

Mathematics

9th - 12th Grade

Practice Problem

Hard

CCSS
HSA.APR.D.6, HSF-IF.C.7D, HSF-IF.C.7E

+2

Standards-aligned

Created by

Amelia Wright

FREE Resource

Standards-aligned

CCSS.HSA.APR.D.6
,
CCSS.HSF-IF.C.7D
,
CCSS.HSF-IF.C.7E
CCSS.HSF.IF.A.2
,
CCSS.HSF-IF.C.7A
,
The video tutorial explains how to find the limit of a rational function as x approaches -1. Initially, direct substitution results in division by zero, so the function is simplified by determining if x + 1 is a factor of the numerator using synthetic division. After confirming x + 1 is a factor, the function is simplified, allowing the limit to be found through direct substitution. The limit is calculated to be -5. The tutorial concludes with a graphical verification, showing the function's graph with a hole at x = -1, confirming the limit is -5.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main challenge when finding the limit of a rational function as x approaches a value that makes the denominator zero?

The numerator becomes zero.

The function becomes undefined due to division by zero.

The function becomes infinite.

The function becomes a constant.

Tags

CCSS.HSF.IF.A.2

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in simplifying a rational function to find its limit?

Determining if a factor of the denominator is also a factor of the numerator.

Finding the derivative.

Performing direct substitution.

Graphing the function.

Tags

CCSS.HSA.APR.D.6

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which method can be used to determine if x + 1 is a factor of the numerator?

Synthetic division

Partial fraction decomposition

Integration

Completing the square

Tags

CCSS.HSA.APR.D.6

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In synthetic division, what is the constant used when dividing by x + 1?

1

-1

2

0

Tags

CCSS.HSA.APR.D.6

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does a remainder of zero indicate in synthetic division?

The divisor is not a factor.

The divisor is a factor.

The function is undefined.

The function has a vertical asymptote.

Tags

CCSS.HSA.APR.D.6

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

After simplifying the rational function, what is the next step to find the limit?

Finding the derivative.

Graphing the function.

Using the quadratic formula.

Performing direct substitution.

Tags

CCSS.HSF-IF.C.7D

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the common factor between the numerator and denominator represent graphically?

A vertical asymptote

A horizontal asymptote

A hole in the graph

A point of intersection

Tags

CCSS.HSF-IF.C.7D

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