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

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Answer 1 · 2015-02-18T23:08:34

Hello !

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

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

Now, apply the transformations :

1) translate this curve one step on the left to obtain $f_{1} (x) = {(x + 1)}^{3}$ $f_1(x) = (x+1)^3$

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

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

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

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

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

How do you use transformations of f(x)=x3f(x)=x^3 to graph the function h(x)=15(x+1)3+2h(x)= 1/5 (x+1)^3+2?