Question

write the equation given the transformation from the parent function y = x vertical dilation that stretches by a factor of 4 and a vertical translation down 5

Explanation:

Step1: Recall vertical dilation rule

For a function \( y = f(x) \), a vertical dilation by a factor of \( a \) (where \( a>0 \)) transforms it to \( y = a \cdot f(x) \). Here, the parent function is \( y = x \) (so \( f(x)=x \)) and the vertical dilation factor is 4. So after dilation, the function becomes \( y = 4x \).

Step2: Recall vertical translation rule

For a function \( y = f(x) \), a vertical translation down by \( k \) units (where \( k>0 \)) transforms it to \( y = f(x)-k \). Here, we need to translate down by 5 units. So we subtract 5 from the dilated function.
Combining the two transformations, the new function is \( y = 4x - 5 \).

Answer:

\( y = 4x - 5 \)