Question

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

Answer 1

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

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