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In the function f(x), x is replaced with 3x.
f(x)=1/2sin(x)−4
What effect does this have on the graph of the function?
A. The graph is vertically stretched by a factor of 1//3.
B. The graph is vertically compressed by a factor of 1/3.
C. The graph is horizontally stretched by a factor of 1/3.
D. The graph is horizontally compressed by a factor of 1/3.

Respuesta :

jorgereyes01

Just took the test, so the answer is...

D. Horizontally compressed by a factor of 1/3

[tex]f(x)=\frac{1}{2}sin(x)-4[/tex] is horizontally compressed by a factor of 1/3 to get [tex]f(x)=\frac{1}{2}sin(3x)-4[/tex]

Option D is correct

What is horizontal compression?

Note that:

If a function [tex]f(x)=Asin(x)[/tex] is transformed to [tex]g(x)=Asin(kx)[/tex], it means that the function f(x) is horizontally compressed by 1/k

Relating this rule to the given function [tex]f(x)=\frac{1}{2}sin(x)-4[/tex]

If x is replaced with 3x, the function will become:

[tex]f(x)=\frac{1}{2}sin(3x)-4[/tex]

This means that the graph of  [tex]f(x)=\frac{1}{2}sin(x)-4[/tex] is horizontally compressed by a factor of 1/3 to get [tex]f(x)=\frac{1}{2}sin(3x)-4[/tex]

Learn more on horizontal compression of graphs here: https://brainly.com/question/2938738