Question

Let f (x) = 8x. The graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 and a translation of 7 units down. What is the equation for g(x)? Enter your answer in the box.

Answer 1

ANSWER

$g(x)=32x-7$

EXPLANATION

We want to find the equation for g(x).

First, the function is stretched vertically by a factor of 4. This means that the function changes as follows:

$f(x)\to4f(x)$

Therefore, the function becomes:

$\begin{gathered} 4(8x) \\ \Rightarrow32x \end{gathered}$

Then, it is translated 7 units down. This means that the function changes as follows:

$f(x)\to f(x)-7$

Therefore, the equation for g(x) is:

$g(x)=32x-7$