Question

Need help with two problems? (Posting them below)

Answer 1

Find the domain and range of the following function \[f(x)=\sqrt[5]{(x-4)}+2\]
I think the domain is (infinity, -infinity) and the range is (2, infinity] ?

Answer 2

And then,
*Describe what each number in equation does to translate this graph from the base graph of \[f(x)=\sqrt[5]{x}\]

Pretty sure they just want me to describe what vertical/horizontal functions happen compared to each function.

Answer 3

You are correct in what they are asking you, what happens to the vertical and horizontal movement compared to the base graph.

The domain is all values that exclude negatives under the radical. The range is all numbers possible once you define your domain.

What values of x would make numbers under the radical negative?

Answer 4

Are you referring to \[f(x)=\sqrt[5]{x-4}+2\] ?
In that case, all numbers less that or equal to 3 would make that radical negative.

Answer 5

That's right or in other words
$$
\sqrt[5]{x-4}+2\\
$$
We need
$$
x-4\ge 0\\
x\ge4
$$
This is your domain
The range then is
$$
y\ge \sqrt[5]{0}+2=0+2=2
$$
Which means your range is
$$
y\ge 2
$$

Answer 6

Ah okay! Well that was simple. Thank you :)

Answer 7

@Maddy1251 just in case u wonder why the domain is x>=4 and not (-infinity, infinity), u can read this:

http://math.stackexchange.com/questions/25528/cubic-root-of-negative-numbers