algebra 2 problem

Question

Could someone help me answer this please find the function of f defined by f (x) = 2x/x^2+8
(a) F(-1) =
(b) F(-x) =
(c) –f(x) =
(d) F(x +h) =
How do I simplify?

Answer 1

Here, we just replace x in our function with whatever is in the parentheses.

a.) f(-1) = 2(-1)/(-1)²+8

= -2/1+8

= -2/9

b.) f(-x) = 2(-x)/(-x)²+8

= -2x/x²+8

Note: If we graphed this function we would see that this is the reflection of the original function about the y-axis.

c.) -f(x) = -(2x/x²+8)

= -2x/x²+8

Note: This is the reflection about the x-axis of the original function. It just so happens to be the same as the reflection about the y-axis for this function.

d.) f(x+h) = 2(x+h)/(x+h)²+8

= (2x + 2h) / (x²+2xh+h²+8)

Note: This function shifts the original function h units to the left. To shift the function to the right you would use a negative number for h.