What is the effect on the graph of the function f(x) = x when f(x) is replaced with −f(x) + 4? a) vertical reflection over x-axis and shifts up 4 units b) vertical reflection over x-axis and shifts right 4 units c) horizontal reflection over y-axis and shifts up 4 units d) horizontal reflection over y-axis and shifts right 4 units

The effects on a graph are represented by transforming the graphs

The true statement is: (a) vertical reflection over x-axis and shifts up 4 units

The functions are given as:

--- the parent function

--- the new function

Make f(x) the subject in

So, we have:

The "-x" implies that the function is reflected across the vertical axis

The "+4" implies that the function is then shifted up by 4 units.

Hence, the true statement is: (a) vertical reflection over x-axis and shifts up 4 units

Read more about function transformations at:

link

f(x) = x  replaced −f(x) + 4

f(x) = - f(x) : vertical reflection over x-axis

4: shifts up 4 units

Answer

A) vertical reflection over x-axis and shifts up 4 units