Question

Help please?

Answer 1

Original expression. `y=x^3-3x`
graph{y=x^3-3x [-5, 5, -5, 5]}

1. `f(x)` translated three units up. New function is `y=x^3-3x+3`
   graph{y=x^3-3x+3 [-5, 5, -5, 6]}

2. `f(x)` shifted two places to the left and three places down. New function is `y=(x+2)^3-3(x+2)-3`

graph{y=(x+2)^3-3(x+2)-3 [-5, 5, -8, 5]}

For any value added to `x`, the function is stated as
`(x-"added value")`
For any value subtracted from `x`, the function is stated as
`(x+"subtracted value")`

In case of `y`
For any value added to `y`, the function is stated as
`(y+"added value")`
For any value subtracted from `x`, the function is stated as
`(y-"subtracted value")`

Note the difference of sign in `x` and `y` respectively.

Compare maximum and minimum in the graphs.
Shifting left `->` subtracting amount of shift from `x`
Opposite for shifting right

Shifting up `->` adding amount of shift to `y`
Opposite for shifting down