Question

Given the parent function f(x)=-4x+7, write the equation of the new function when f(x) is shifted up 4 units then reflected across the y-axis.

Answer 1

Check the template in the picture below.

`f(x)=-4x+7\hspace{5em} \begin{array}{ccccccccllllllll} &A&B&&C&D \\ f(x)=&-4(&1&x&+0)&+7\\ shifted&&-1&&&+4\\ &-4(&-1&x&+0)&+11 \end{array}\\\\ ~\hspace{17em}-4(-x)+11\\\\ ~\hspace{14em}f(x) = 4x+11`

notice, for the reflection across the y-axis we simply make B negative, and for the shift we simply add 4 to D.