Question

Find domain and range of the function
\sqrt{x} + 14

Domain:
Range:
Write the answer in interval notation.
Note: If the answer includes more than one interval write the intervals separated by the union symbol, U. If needed enter -\infty as - infinity and \infty as infinity .

Please explain how to find the answer!

Answer 1

f(x) = rootx + 14?

Answer 2

\(f(x)=\sqrt{x} + 14\) is a vertical shift of \(f(x)=\sqrt{x}\).

Do you know what the graph of \(f(x)=\sqrt{x}\) looks like?

Answer 3

x can be anything , so domain and range are both (\[(-\infty , \infty)\]

Answer 4

no, definitely not.

Answer 5

Both domain and range are bounded.

Answer 6

oh , sorry my bad , forgot the root

Answer 7

You can either do this algebraically, or graphically. Kind of depends on what you've been shown and which you understand better.

Algebraically, domain is what x's are "allowed' to be put into the function. Since you have a square root expression here, you need to make sure what's under it is non-negative.

Answer 8

Range is what y's you can get "out of" the function. Again, the sq root is important here - you only get nonnegatives from a sq. root, but then here, you are adding 14 to that.

Answer 9

rootx therefore , domain is positive , \[[0 , \infty)\],
range is \[[14 , \infty)\]

Answer 10

Graphically: