Question

What is the effect on the graph of the function f(x) = x when f(x) is replaced with -1/2 f(x)?

Answer 1

Answer:

The correct option is B.

Step-by-step explanation:

The given function is

$f(x)=x$

The new function is

$g(x)=-\frac{1}{2}f(x)$

$g(x)=-\frac{1}{2}x$        .... (1)

It is in the form of

$g(x)=mx$                   .... (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

$m=-\frac{1}{2}$

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.