Question

What is the effect on the graph of the function f(x) = x when f(x) is replaced with −f(x) + 5?

Answer 1

The function f(x) translated left by 5 units and then it is reflected across the x-axis.

Explanation:

The original equation of the graph of the function is f(x) = x ........ (1)

If we replace f(x) by [- f(x) + 5] then the equation becomes - f(x) + 5 = x

⇒ f(x) = - (x - 5) ..... (2)

So, comparing equations (1) and (2), we can conclude that the graph of the function f(x) translated left by 5 units and then it is reflected across the x-axis. (Answer)