Answer:
Option B
[tex]g(x) = -6x^2[/tex]
Step-by-step explanation:
If the graph of the function [tex]g(x)=cf(x)[/tex] represents the transformations made to the graph of [tex]y= f(x)[/tex] then, by definition:
If [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor c.
If [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor c
If [tex]c <0[/tex] then the graph is reflected on the x axis.
In this problem we have the function [tex]f(x)=x^2[/tex]
We now that this function is vertically stretched by a factor of 6 to g(x) and reflected over the x-axis
Then [tex]|c| =6 >0[/tex] and [tex]c=-6<0[/tex]
Therefore the graph of [tex]g(x)[/tex] is [tex]g(x) = -6f(x)[/tex]
[tex]g(x) = -6x^2[/tex]
