146k views
4 votes
The function f(x) is multiplied by a factor of 2 and then 3 is added to the function.

f(x) = sin(x)
What effect does this have on the graph of the function?

A.) The graph is vertically compressed by a factor of 3 and shifted up 2 units.
B.) The graph is vertically stretched by a factor of 3 and shifted up 2 units.
C.) The graph is vertically compressed by a factor of 2 and shifted up 3 units.
D.) The graph is vertically stretched by a factor of 2 and shifted up 3 units.

User ElKePoN
by
7.9k points

2 Answers

5 votes

Answer:

D.) The graph is vertically stretched by a factor of 2 and shifted up 3 units

Explanation:

best of luck to you all~! You are the best <3

User Bernardo Duarte
by
7.9k points
3 votes

Given:

The function is:


f(x)=\sin x

The function f(x) is multiplied by a factor of 2 and then 3 is added to the function.

To find:

The effect on the graph of the function.

Solution:

The transformation is defined as


g(x)=kf(x)+b .... (i)

Where, k is stretch factor and b is vertical shift.

If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

It is given that the function f(x) is multiplied by a factor of 2 and then 3 is added to the function. So, the new function is:


g(x)=2f(x)+3 ...(ii)

On comparing (i) and (ii), we get


k=2, it means the graph is vertically stretched by a factor of 2.


b=3, it means the graph is shifted up 3 units.

Therefore, the correct option is D.

User Robert Echlin
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.