MATH SOLVE

5 months ago

Q:
# Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). f(x) = 4 cos x ; g(x) = cos x Select one:a. Vertical stretch by a factor of 4b. Horizontal stretch by a factor of 4c. Vertical shrink by a factor of 1/4d. Horizontal shrink by a factor of 1/4

Accepted Solution

A:

Answer:Option aStep-by-step explanation:If the graph of the function [tex]y=f(x)=cg(hx)[/tex] represents the transformations made to the graph of [tex]y= g(x)[/tex] then, by definition:If [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor c.If [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor cIf [tex]c <0[/tex] then the graph is reflected on the x axis.If [tex]0 <h <1[/tex] the graph is stretched horizontally by a factor [tex]\frac{1}{h}[/tex]If [tex]h> 1[/tex] the graph is compressed horizontally by a factor [tex]\frac{1}{h}[/tex]In this problem we have the function [tex]f(x)=4cos(x)[/tex] and our parent function is [tex]g(x)= cosx[/tex]therefore it is true that [tex]c=4[/tex] so [tex]c>1[/tex] and [tex]h =1[/tex]Therefore the graph of [tex]y=cosx[/tex] is stretched vertically by a factor c = 4 The answer is "Vertical stretched by a factor of 4"