Question

Let f(x) = −x^3 − 8x^2 − 9x + 11. Identify the function g that reflects f across

the y-axis.

Answer 1

`g(x)=x^3-8x^2+9x+11`

Explanation:

`f(x)=-x^3-8x^2-9x+11`

When a function is reflected across the y-axis, negative x-values become positive, and positive x-values become negative.

Therefore, substitute -x in place of x in the function f(x):

`g(x)=-(-x)^3-8(-x)^2-9(-x)+11`

We know that
`(-x)^3=-(x^3)`

`\implies -(-x)^3=--(x^3)=x^3`

We know that
`(-x)^2=x^2`

`\implies -8(-x)^2=-8(x)^2=-8x^2`

Also
`-9(-x)=+ \ 9x`

Therefore,

`g(x)=x^3-8x^2+9x+11`