Question

How do you sketch the graph `g(x)=-x^5-3` and `f(x)=x^5` using transformations and state the domain and range of g?

Answer 1

`g(x) = -f(x) - 3` Domain and range = `RR`

Explanation:

If you know x^5 is like x^3 but is not like x^1 because it's not a straight line, then

`f(x) = x^5` Domain and range = `RR`
`(x,y) mapsto (x,-y)` Reflection on 0y axis.
`(x, -y) mapsto (x, -y - 3)` Vertical translaction `y := y - 3`