Question

IM BEING TIMED, WILL GIVE 25 POINTS (NEEDED WITHIN THE NEXT 20 MINUTES The graph g(x)=x^3-x is shown. (idk how to screenshot, so please pull it up on the desmos graphing website or something) What will the graph of 0.5g(x-2)+1 look like?

Answer 1

The function is

`f(x)=0.5x^3-3x^2+5.5x-2`

The graph is attached.

Explanation:

We have a function g(x) and we need to graph a new function that is function of g(x).

The final function is

`f(x)=0.5\cdot g(x-2)+1`

We start by calculating g(x-2):

`g(x-2)=(x-2)^3-(x-2)\\\\g(x-2)=(x^3-6x^2+12x-8)-(x-2)\\\\g(x-2)=x^3-6x^2+11x-6`

Then, we can calculate f(x) as:

`f(x)=0.5\cdot g(x-2)+1\\\\g(x-2)=x^3-6x^2+11x-6\\\\\\f(x)=0.5(x^3-6x^2+11x-6)+1\\\\f(x)=0.5x^3-3x^2+5.5x-3+1\\\\\\f(x)=0.5x^3-3x^2+5.5x-2`