What is the effect on the graph of the function f(x) = x when f(x) is replaced with -1/2 f(x)? a) vertical reflection over x-axis and vertical stretch b) vertical reflection over x-axis and vertical compression c) horizontal reflection over y-axis and horizontal stretch d) horizontal reflection over y-axis and horizontal compression

The correct option is B.

Step-by-step explanation:

The given function is

The new function is

       .... (1)

It is in the form of

                  .... (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

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.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

astronomers is your final answer! : )