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

Feb 18, 2015

Hello !

You know very well the graph of $f \left(x\right) = {x}^{3}$ :

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

Now, apply the transformations :

1) translate this curve one step on the left to obtain ${f}_{1} \left(x\right) = {\left(x + 1\right)}^{3}$

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

2) Dilate this new curve with coefficient $\setminus \frac{1}{5}$ to obtain ${f}_{2} \left(x\right) = \setminus \frac{1}{5} {\left(x + 1\right)}^{3}$

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

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

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