Question

How do you graph `y= 2( x - 4) ^ { 3} + 5`?

Answer 1

The graph of `y` is the standard graph of `f(x)=x^3` shifted positive in `x` by 4 units, scaled by 2 and shifted positive in `y` by 5 units,

Explanation:

Consider the standard graph of `f(x)=x^3` below.

graph{x^3 [-22.81, 22.8, -11.4, 11.4]}

Given `y = 2(x-4)^3+5`

Then `y = 2*f(x-4)+5`

Hence, the graph of `y` is the standard graph of `f(x)=x^3` shifted positive ("right") in `x` by 4 units, scaled by 2 and shifted positive ("up") in `y` by 5 units,

The transformations above will produce the graph of `y` below.

graph{2(x-4)^3+5 [-22.81, 22.8, -11.4, 11.4]}