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

Answer:

The function is:

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

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

$y = cf(x)$ Where $0$.

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 $h$  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 $k$  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 $\frac{1}{4}$ and moves the function 3 units to the right and 2 units up then the transformation is:

$y=\frac{1}{4}f(x-3)+2$

The function is:

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