Let's analyze each function to determine which of them is a power function.

A power function is typically of the form $f(x) = ax^n$, where $a$ is a constant and $n$ is a real number (positive or negative).

• $y = \frac{3}{x^2 + 5}$: This is not a power function because it involves a rational expression where $x^2$ is in the denominator and part of a sum with 5.

• $g(x) = 9x^{-7}$: This is a power function. It fits the form $ax^n$ with $a = 9$ and $n = -7$.

• $f(s) = -s$: This is a power function. It can be rewritten as $f(s) = -1 \cdot s^1$, fitting the form $ax^n$ with $a = -1$ and $n = 1$.

• $y = \frac{2}{7} \sqrt{x}$: This is a power function. We can rewrite it as $y = \frac{2}{7} x^{1/2}$, where $a = \frac{2}{7}$ and $n = \frac{1}{2}$.

• $p(x) = 58x^5$: This is a power function. It fits the form $ax^n$ with $a = 58$ and $n = 5$.

Correct answers:

• $g(x) = 9x^{-7}$
• $f(s) = -s$
• $y = \frac{2}{7} \sqrt{x}$
• $p(x) = 58x^5$

The only function that is not a power function is $y = \frac{3}{x^2 + 5}$.

Would you like more details or have any questions?
Here are some related questions:

1. What is the difference between a power function and a polynomial function?
2. Can power functions have fractional exponents?
3. How do negative exponents affect the graph of power functions?
4. Can a power function have a variable in the denominator?
5. What are the real-world applications of power functions?

Tip: Remember that a power function strictly involves a single term of the form $ax^n$, without additions or subtractions involving the variable.