Answer:
The graph of [tex]y=cos(x)[/tex] is:
*Stretched vertically by a factor of 3
*Compressed horizontally by a factor [tex]\frac{1}{10}[/tex]
*Moves horizontally [tex]\pi[/tex] units to the rigth
The transformation is:
[tex]y=3f(10(x-\pi))[/tex]
Step-by-step explanation:
If the function [tex]y=cf(h(x+b))[/tex] represents the transformations made to the graph of [tex]y= f(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 c
If [tex]c <0[/tex] then the graph is reflected on the x axis.
If [tex]b> 0[/tex] The graph moves horizontally b units to the left
If [tex]b <0[/tex] The graph moves horizontally b units to the rigth
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]y=3cos(10(x-pi))[/tex] and our parent function is [tex]y = cos(x)[/tex]
The transformation is:
[tex]y=3f(10(x-\pi))[/tex]
Then [tex]c =3>1[/tex] and [tex]b =-\pi < 0[/tex] and [tex]h=10 > 1[/tex]
Therefore the graph of [tex]y=cos(x)[/tex] is:
Stretched vertically by a factor of 3.
Also as [tex]h=10[/tex] the graph is compressed horizontally by a factor [tex]\frac{1}{10}[/tex] .
Also, as [tex]b =-\pi < 0[/tex] The graph moves horizontally [tex]\pi[/tex] units to the rigth
