Answer:
The correct option is B.
Step-by-step explanation:
The given function is
[tex]f(x)=x[/tex]
The new function is
[tex]g(x)=-\frac{1}{2}f(x)[/tex]
[tex]g(x)=-\frac{1}{2}x[/tex] .... (1)
It is in the form of
[tex]g(x)=mx[/tex] .... (2)
Where, m is a constant.
If m is negative, then there is a vertical reflection over x-axis. If the constant is greater than 1, we get a vertical stretch and if the constant is between 0 and 1, we get a vertical compression.
From (1) and (2), we get
[tex]m=-\frac{1}{2}[/tex]
Since the value of m is negative and absolute value of m is between 0 and 1, therefore the graph g(x) shows the vertical reflection over x-axis and vertical compression.
Option B is correct.
