Question

Cube Root Function Question! 15 points!

The graph of h(x) is a translation of f (x) = Root Index 3
Which equation represents h(x)?

Answer 1

Answer: Second option.

Explanation:

Below are some transformations for a function f(x) :

1. If
`f(x)+k`, the function is shifted "k" units up.

2. If
`f(x)-k`, the function is shifted "k" units down.

3. If
`f(x-k)`, the function is shifted "k" units right.

4. If
`f(x+k)`, the function is shifted "k" units left.

The Cube root parent function is:

`f(x)=\sqrt[3]{x}`

By definition, the graph of this function passes through the origin, as you can observe in the picture attached.

In this case, you need to analize the graph given in the exercise. You can see that the the graph of the function h(x) is like the parent function f(x), but shifted 2 units left.

Therefore, based on the transformations explained above, you can determine that the equation of the function h(x) is the following:

`h(x)=f(x+2)\\\\h(x)=\sqrt[3]{x+2}`