Question

The parent function, f(x) = 5x, has been vertically compressed by a factor of one-fourth, shifted to the right three units and up two units. Choose the correct function to represent the transformation

Answer 1

The function is:

`y=(5)/(4)(x-3) +2\\`

Explanation:

If we have a function f(x) and we want to compress its graph vertically c units then we must do the transformation

`y = cf(x)` Where
`0 <c <1`.

If we want to make a transformation that moves horizontally h units the graph of f(x) then we must do:

`y = f (x + h)`

If
`h> 0` the graph of f(x) shifts h units to the left

If
`h <0` 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

`y = f (x) + k`

If
`k> 0` the graph of f(x) moves k units up

If
`k <0` the graph of f(x) shifts k units down

In this case
`f (x) =5x`

If the transformation vertically compresses the function by a factor of
`(1)/(4)` and moves the function 3 units to the right and 2 units up then the transformation is:

`y=(1)/(4)f(x-3)+2`

The function is:

`y=(5)/(4)(x-3) +2\\`