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Understanding Limits of Piece-Wise Functions

Understanding Limits of Piece-Wise Functions

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Practice Problem

Hard

CCSS
HSF.IF.A.2, HSF-IF.C.7B

Standards-aligned

Created by

Sophia Harris

FREE Resource

Standards-aligned

CCSS.HSF.IF.A.2
,
CCSS.HSF-IF.C.7B
The video tutorial explores the concept of limits using a piece-wise defined function. It examines the limits as X approaches 1 and 3, demonstrating how to determine if a limit exists by evaluating the function from both sides. The tutorial uses both analytical and graphical methods to explain why the limit at X=1 does not exist and how the limit at X=3 can be determined through direct substitution.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the equation of the graph when x is less than 1?

Y = 3X - 2

Y = X + 1

Y = -X - 1

Y = 2X - 1

Tags

CCSS.HSF-IF.C.7B

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the equation of the graph when x is greater than or equal to 1?

Y = 3X - 2

Y = X + 1

Y = -X - 1

Y = 2X - 1

Tags

CCSS.HSF-IF.C.7B

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the function value as x approaches 1 from the left?

2

0

-2

1

Tags

CCSS.HSF.IF.A.2

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the function value as x approaches 1 from the right?

1

-2

0

2

Tags

CCSS.HSF.IF.A.2

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why does the limit not exist at x = 1?

The function is undefined at x = 1

The function has a vertical asymptote at x = 1

The function values from the left and right are different

The function is continuous at x = 1

Tags

CCSS.HSF.IF.A.2

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the function value as x approaches 3?

-1

-4

-3

-2

Tags

CCSS.HSF.IF.A.2

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How can the limit as x approaches 3 be determined?

By using L'Hôpital's rule

By direct substitution

By evaluating both sides separately

By finding the derivative

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