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

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

$f(x)=\frac{5}{4}x$

shift right 3 units, minus 3 from every x

$f(x)=\frac{5}{4}(x-3)$

shift up 2 units so add 2 to whole function

$f(x)=\frac{5}{4}(x-3)+2$

if you expand it you get

$f(x)=\frac{5}{4}x-\frac{7}{4}$