Question

How do you sketch the graph `g(x)=(x+1)^5+10` and `f(x)=x^5` using transformations and state the domain and range of g?

Answer 1

See below for an explanation!

Explanation:

This is what `f(x)` look like:

graph{x^5 [-10, 10, -5, 5]}

`g(x)` is translated 1 unit to the left and 10 units up:

graph{((x+1)^5)+10 [-20, 20, -2, 18]}

The domain and range of `g(x)` will both be `(-oo,oo)`. The graph will continue in both directions for infinity without anything to block the graph.