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

1 Answer
May 16, 2018

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]}