Question

Given the function, fx=x+4 a).Write the transformed equation g(x), if g(x) = -f(x) + 2. b). Describe the transformation(s) that takes place. i. What does the -f(x) do to the function? ii. What does the +2 do to the function?

Answer 1

Since the given function is

$f(x)=x+4$

Since the function after transformation is

$g(x)=-f(x)+2$

Then we will find g(x) by substituting f(x) by (x + 4)

$g(x)=-(x+4)+2$

Simplify it

$\begin{gathered} g(x)=-(x)+-(4)+2 \\ \\ g(x)=-x-4+2 \\ \\ g(x)=-x-2 \end{gathered}$

a) The transformed equation is

$g(x)=-x-2$

b)

When we change the sign of f(x), that means we made a reflection on the x-axis

i. -f(x) means reflect f(x) about the x-axis

When we add f(x) by a number, then that means we translate the f(x) by a number

ii. +2 means translate the function 2 units up