Question

How do you use transformations of `f(x)=x^3` to graph the function `h(x)= 1/5 (x+1)^3+2`?

Answer 1

Hello !

You know very well the graph of `f(x) = x^3` :

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

Now, apply the transformations :

1) translate this curve one step on the left to obtain `f_1(x) = (x+1)^3`

graph{(x+1)^3 [-10, 10, -5, 5]}

2) Dilate this new curve with coefficient `\frac{1}{5}` to obtain `f_2(x) = \frac{1}{5}(x+1)^3`

graph{1/5*(x+1)^3 [-10, 10, -5, 5]}

3) Finally, translate this new curve 2 steps on the top to obtain `h(x)=\frac{1}{5}(x+1)^3+2`

graph{1/5*(x+1)^3+2 [-10, 10, -5, 5]}