What transformations are needed to change the parent cosine function to y=3cos(10(x-pi))?

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 rigthThe 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 leftIf [tex]b <0[/tex] The graph moves horizontally b units to the rigthIf [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