Question

If f(x) = x^2 is vertically stretched by a factor of 6 to g(x) and reflected over the x-axis, what is the equation for g(x)?

Answer 1

Answer:

Option B

$g(x) = -6x^2$

Step-by-step explanation:

If the graph of the function $g(x)=cf(x)$  represents the transformations made to the graph of $y= f(x)$  then, by definition:

If  $0$ then the graph is compressed vertically by a factor c.

If  $|c| > 1$ then the graph is stretched vertically by a factor c

If $c$  then the graph is reflected on the x axis.

In this problem we have the function $f(x)=x^2$  

We now that this function  is vertically stretched by a factor of 6 to g(x) and reflected over the x-axis

Then  $|c| =6 >0$  and $c=-6$

Therefore the graph of $g(x)$ is $g(x) = -6f(x)$

$g(x) = -6x^2$