A. We can compress the graph of the function [tex]f(x)=|x|[/tex] in the y-direction by multiplying the whole function by a constant C, such that [tex]0<C<1.[/tex] Since [tex]0<0.6<1,[/tex], the graph of the function [tex]g(x)= 0.6|x|[/tex] is obtained from the graph of the function [tex]f(x)=|x|[/tex] by compression in the y-direction.
B. We can stretch the graph of the function [tex]f(x)=|x|[/tex] in the y-direction by multiplying the whole function by a constant C, such that [tex]C>1.[/tex] Since [tex]4>1,[/tex], the graph of the function [tex]g(x)= 4|x-3|[/tex] is obtained from the graph of the function [tex]f(x)=|x|[/tex] by compression in the y-direction and translation 3 units to the right.
C. We can flip the graph of the function [tex]f(x)=|x|[/tex] upside down by multiplying the whole function by −1, then translate 1 unit to the left and 5 units up. Then we will get the function [tex]g(x)=-|x+1|+5.[/tex]
