Question

The graph of g(x)=x^3 -x is shown.

(picture 1)

Which is the graph of .5g(x-2)+1
(answer choices pics 2-5)

Answer 1

Graph 4 is the right answer.

Explanation:

Given
`g(x) =x^(3)-x`

So,
`5g(x-2) +1 = 5[(x-2)^(3)-(x-2) ] +1 = 5(x-2)^(3) -5x +11` ....... (1)

The graph 2 shows that the function should pass through (0,-2) but the point does not satisfy equation (1).

Graph 3 again shows that the function should pass through (0,-2) point but the point does not satisfy equation (1).

Graph 4 shows that the function should pass through the point (1,1) and this point satisfies the equation (1).

And graph 5 shows that the function should pass through the point (-1,-1) but this point does not satisfy the equation (1).

Therefore, the graph 4 is of [5g(x-2) +1].