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Understanding Limits and Horizontal Asymptotes

Understanding Limits and Horizontal Asymptotes

Assessment

Interactive Video

Mathematics

9th - 12th Grade

Practice Problem

Hard

CCSS
HSF-IF.C.7D, HSF-IF.C.7E

Standards-aligned

Created by

Ethan Morris

FREE Resource

Standards-aligned

CCSS.HSF-IF.C.7D
,
CCSS.HSF-IF.C.7E
The video tutorial explains how to use the graph of a function, f(x), to determine limits as x approaches positive and negative infinity. It also covers how to find the equations of horizontal asymptotes by evaluating these limits. The tutorial demonstrates that as x approaches positive infinity, the function approaches a y-value of -3, and as x approaches negative infinity, it approaches a y-value of 3. These values correspond to the horizontal asymptotes y = -3 and y = 3, respectively.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the primary focus of the video tutorial?

Learning about derivatives

Exploring the concept of limits and horizontal asymptotes

Studying the properties of integrals

Understanding vertical asymptotes

Tags

CCSS.HSF-IF.C.7E

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

As x approaches positive infinity, what value does f(x) approach?

Negative three

Positive three

Positive infinity

Zero

Tags

CCSS.HSF-IF.C.7D

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the horizontal asymptote as x approaches positive infinity?

y = infinity

y = -3

y = 3

y = 0

Tags

CCSS.HSF-IF.C.7E

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

As x approaches negative infinity, what value does f(x) approach?

Negative three

Zero

Positive three

Negative infinity

Tags

CCSS.HSF-IF.C.7D

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the horizontal asymptote as x approaches negative infinity?

y = infinity

y = 3

y = 0

y = -3

Tags

CCSS.HSF-IF.C.7D

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How are horizontal asymptotes determined from limits?

By using the midpoint theorem

By calculating the integral

By finding the derivative

By evaluating the limits at infinity

Tags

CCSS.HSF-IF.C.7D

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the equation of the horizontal asymptote when the limit of f(x) as x approaches infinity is negative three?

y = infinity

y = 0

y = -3

y = 3

Tags

CCSS.HSF-IF.C.7D

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