Question

The graph of g(x)=x^3-x is shown. Which is the graph of .5g(x-2)+1?

Answer 1

We have the function,
`g(x)=x^(3)-x`.

It can be seen that various transformations are applied to the function g(x) in order to obtain the new function.

As the new function is
`0.5g(x-2)+1` i.e.
`(1)/(2)g(x-2)+1`

We get that,

The function g(x) is translated to the right by 2 units, then g(x) ⇒ g(x-2).

Further, g(x-2) is shrinked vertically by
`(1)/(2)`, which gives g(x-2) becomes
`(1)/(2)g(x-2)`.

Finally, the function
`(1)/(2)g(x-2)` is translated 1 unit upwards, then
`(1)/(2)g(x-2)` ⇒
`(1)/(2)g(x-2)+1`

Hence, the graph of the new function is given below.