Answer:
The function is:
[tex]y=\frac{5}{4}(x-3) +2\\[/tex]
Step-by-step explanation:
If we have a function f(x) and we want to compress its graph vertically c units then we must do the transformation
[tex]y = cf(x)[/tex] Where [tex]0 <c <1[/tex].
If we want to make a transformation that moves horizontally h units the graph of f(x) then we must do:
[tex]y = f (x + h)[/tex]
If [tex]h> 0[/tex] the graph of f(x) shifts h units to the left
If [tex]h <0[/tex] the graph of f(x) shifts h units to the right.
If we want to make a transformation that moves vertically k units the graph of f(x) then we must do
[tex]y = f (x) + k[/tex]
If [tex]k> 0[/tex] the graph of f(x) moves k units up
If [tex]k <0[/tex] the graph of f(x) shifts k units down
In this case [tex]f (x) =5x[/tex]
If the transformation vertically compresses the function by a factor of [tex]\frac{1}{4}[/tex] and moves the function 3 units to the right and 2 units up then the transformation is:
[tex]y=\frac{1}{4}f(x-3)+2[/tex]
The function is:
[tex]y=\frac{5}{4}(x-3) +2\\[/tex]
