to vertically compress a function, f(x) by a factor of d, we multiply the whole function by d, so f(x) becomes d*f(x)
to shift a function to the right by c units, subtract c from every x
so f(x) becomes f(x-c)
to shift a function up by c units, add c to the whole function
so f(x) becomes f(x)+c
ok, given f(x)=5x
vertically compress by 1/4, multiply whole thing by 1/4
[tex]f(x)=\frac{5}{4}x[/tex]
shift right 3 units, minus 3 from every x
[tex]f(x)=\frac{5}{4}(x-3)[/tex]
shift up 2 units so add 2 to whole function
[tex]f(x)=\frac{5}{4}(x-3)+2[/tex]
if you expand it you get
[tex]f(x)=\frac{5}{4}x-\frac{7}{4}[/tex]
