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Understanding the Domain of a Square Root Function

Understanding the Domain of a Square Root Function

Assessment

Interactive Video

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•
CCSS
8.F.A.1, HSA.REI.D.12, HSA.APR.C.4

+4

Standards-aligned

Created by

Amelia Wright

FREE Resource

Standards-aligned

CCSS.8.F.A.1
,
CCSS.HSA.REI.D.12
,
CCSS.HSA.APR.C.4
CCSS.HSF-IF.C.7B
,
CCSS.8.EE.B.5
,
CCSS.HSF-IF.C.7A
,
CCSS.HSF.IF.B.5
,
The video tutorial explains how to determine the domain of the function f(x) = √(y² - x²). It discusses the necessity for the radicand to be non-negative, leading to the inequality y² - x² ≥ 0. The tutorial demonstrates factoring the expression as a difference of squares and solving the inequality by considering cases where the product is zero, positive, or negative. It then shows how to graph the lines y = x and y = -x, and identify regions A and C as part of the domain. The video concludes by verifying the domain using a graph of the function.

Read more

10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What must be true about the expression under the square root for the function to be real?

It must be zero.

It must be positive.

It must be non-negative.

It must be negative.

Tags

CCSS.HSA.APR.C.4

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of factoring the expression y^2 - x^2?

(y + x)(y + x)

(y - x)(y - x)

(y + x)(y - x)

(y - x)(y + x)

Tags

CCSS.HSF-IF.C.7B

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which lines are included in the domain of the function?

y = x and y = -x

y = x and y = y

y = -x and y = 0

y = x and y = 0

Tags

CCSS.8.EE.B.5

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the slope of the line y = -x?

2

0

-1

1

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the vertical intercept of the line y = x?

2

-1

0

1

Tags

CCSS.HSA.REI.D.12

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In which region do both inequalities y > x and y > -x hold true?

Region D

Region C

Region B

Region A

Tags

CCSS.HSA.REI.D.12

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of solving the inequality y < x?

Shade below the line y = x

Shade below the line y = -x

Shade above the line y = x

Shade above the line y = -x

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

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