Question

How do you graph `g( x ) = ( x - 2) ^ { 5} - 3`?

Answer 1

graph{(x-2)^5-3 [-10, 10, -5, 5]}

Explanation:

let `t=(x-2)`
`=>`
`g(t)=t^5-3`

I know how to graph the `g(t)` because `a^5+b` looks somewhat similar to `a^3+b`

for `t=0 => g(0)=-3`
for `g(t)=0 => t^5-3=0 iff t=""^5 sqrt(3)~=1.24573094` (using calculator)

so the graph of `g(t)` will look like this:
graph{x^5-3 [-10, 10, -5, 5]}

now, because we were been asked to give our answer in `x`, so let's look:
if `t=(x-2)` we need to take our graph above (of `g(t)`) two steps to the right
(Because: if we have x-A, we goes right A times, and if we have x+A we goes left A times)

so this is the graph of `g(x)` will look like this:
graph{(x-2)^5-3 [-10, 10, -5, 5]}