type the correct answer in each box. use numerals instead of words. function g is a transformation of…

Explanation:

Step1: Observe the vertical stretch

The graph of $g(x)$ is a vertical stretch of $f(x)$ about the $x -$axis. When a function $y = f(x)$ is vertically stretched by a factor $a$, the new function is $y=af(x)$.

Step2: Find the stretch - factor

Notice that for a given $x$ - value (e.g., $x = 1$), the $y$ - value of $g(x)$ is $- 3$ and the $y$ - value of $f(x)$ is $1$. The ratio of the $y$ - values of $g(x)$ and $f(x)$ for the same $x$ - value gives the stretch - factor. The factor $a=\frac{g(x)}{f(x)}$. When $x = 1$, $g(1)=-3$ and $f(1) = 1$, so $a=-3$.

Answer:

$-3$