Question

Having A really hard time and my Professor is being a A Hole with help so can someone just solve it for me I need the range and the graph.​

Answer 1

Normally, when
`x=3` the function

`f(x)=\frac12(x-1)^3-1`

takes on a value of

`f(3)=\frac12(3-1)^3-1=\frac82-1=4-1=3`

so the graph of
`f(x)` passes through the point (3, 3). This is the only place at which the cubic takes on a value of 3, since
`f(x)` is one-to-one.

In the definition of
`q(x)`, however, we remove this point from the curve and replace with the point (3, -2).

While
`f(x)` is a standard cubic function, so that its range is all real numbers, the replacement made for
`q(x)` removes 3 from the range set, so that the range of
`q(x)` would be all real numbers *except* 3.