Translating functions Quiz 1

Question 1

What will be the translated function $$g\left( x ight)$$ of the given function $$f\left( x ight)$$ in the given figure. $$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/e2bacaad-4911-422a-8a20-d9c40d8982594180678590358150176.png"/>

Accepted Answer

$${{\left( x+4 \right)}^{3}}+8$$

Answer

$${{\left( x+6 \right)}^{3}}+8$$

Answer

$${{\left( x-6 \right)}^{3}}+8$$

Answer

$${{\left( x-4 \right)}^{3}}+8$$

Question 2

What is the root common to $$f\left( x ight)={{x}^{2}}+x-2$$ and the function $$g\left( x ight)$$ after translating $$f\left( x ight)$$ three units to the left. $$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/c3bf547c-aedc-403a-80db-663dfd4f0e739215437733421026294.png"/>

Accepted Answer

$$\left( -2,0 \right)$$

Answer

$$\left( -1,0 \right)$$

Answer

$$\left( 1,0 \right)$$

Answer

$$\left( 2,0 \right)$$

Question 3

In the given graph below, $$g\left( x ight)$$ is the translated function of $$f\left( x ight)$$. What is the area of the shaded region? $$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/42daba5e-3bc0-48b6-850c-980508eed3ad5527985868338210351.png"/>

Accepted Answer

$$6$$

Answer

$$8$$

Answer

$$4$$

Answer

$$2$$

Question 4

Find the point of intersection between $$f\left( x ight)={{x}^{2}}-	ext{5}$$ and the curve when $$f\left( x ight)$$ is translated three to the left.

Accepted Answer

$$\left( -1.5,-2.75 \right)$$

Answer

$$\left( -1.7,-2.67 \right)$$

Answer

$$\left( -1.5,-1.07 \right)$$

Answer

$$\left( -1.7,-1.54 \right)$$

Question 5

From the figure given below, what will be the extreme points of $$f\left( x ight)={{\left( -3+\sqrt{x} ight)}^{2}}$$and $$g\left( x ight)$$ which is translated 2 units left respectively.  $$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/e3ff7add-df70-4c8a-9fa8-7180ab12b1e31377621690523154084.png"/>

Accepted Answer

Extreme points of $$f\left( x ight)={{\left( -3+\sqrt{x} ight)}^{2}}\ 	ext{is 9, }g\left( x ight)={{\left( -3+\sqrt{\left( x+2 ight)} ight)}^{2}}	ext{ is 7}	ext{.}$$

Answer

Extreme points of  $$f\left( x ight)={{\left( -3+\sqrt{x} ight)}^{2}}\ 	ext{is 10, }g\left( x ight)={{\left( -3+\sqrt{\left( x+2 ight)} ight)}^{2}}	ext{ is 8}	ext{.}$$

Answer

Extreme points of  $$f\left( x ight)={{\left( -3+\sqrt{x} ight)}^{2}}\ 	ext{is 8, }g\left( x ight)={{\left( -3+\sqrt{\left( x+2 ight)} ight)}^{2}}	ext{ is 6}	ext{.}$$

Answer

Extreme points of  $$f\left( x ight)={{\left( -3+\sqrt{x} ight)}^{2}}\ 	ext{is 10, }g\left( x ight)={{\left( -3+\sqrt{\left( x+2 ight)} ight)}^{2}}	ext{ is 6}	ext{.}$$