What is the effect on the graph of the function f (x) = x when f (x) is replaced with - f (x) + 4

Answer: Reflected about y axis and vertically up by 4.

Step-by-step explanation:

f (x) = x

for - f (x) it becomes - f (x) = - x ... (1) [ multiplying by - 1 both sides ]

to find - f (x) + 4, we add 4 both sides of equation (1), we get

-f (x) + 4 = - x + 4 ... (2)

therefore on applying two transformation [ first reflection about Y axis and translated 4 units upwards makes the function - x+4