https://file.aiquickdraw.com/mathbot/file/1726373921184tx2kfn2v.jpg

The function provided is:

\[
f(x) = 5 \sqrt{x + 15} - 1
\]

### To find the domain:

1. Since there is a square root function involved, the expression inside the square root, \(x + 15\), must be non-negative (greater than or equal to 0) because the square root of a negative number is not real.

2. Set up the inequality:
   \[
   x + 15 \geq 0
   \]
   
3. Solve for \(x\):
   \[
   x \geq -15
   \]

### Domain:
The domain of the function is all \(x\) values such that \(x \geq -15\).

In **interval notation**, the domain is:
\[
[-15, \infty)
\]

Would you like a more detailed explanation or any clarifications?

Here are 5 related questions you might find helpful:
1. How do we find the domain of a function with a cube root?
2. What happens if the function had a logarithm instead of a square root?
3. Can you explain how to find the range of this function?
4. What would be the domain if the square root was in the denominator?
5. How does the transformation \(5 \sqrt{x + 15} - 1\) affect the graph of the square root function?

**Tip:** Always check for restrictions like square roots, denominators, and logarithms when determining the domain of a function.

Find the domain of the following function. Do not use a graphing calculator.

f(x) = 5√(x + 15) - 1

Determine the domain of the square root function f(x) = 5√(x + 15) - 1 by solving the inequality x + 15 ≥ 0. Learn how square roots restrict the domain of functions. Suitable for Grades 9-11.

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