Evaluate the function f left parenthesis r right parenthesis equals StartRoot r plus 7 EndRoot plus 9 at the given values of the independent variable and simplify.
a.  f left parenthesis negative 7 right parenthesis      b.  f left parenthesis 9 right parenthesis      c.  f left parenthesis x minus 7 right parenthesis
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Part 1
a.  f left parenthesis negative 7 right parenthesisequals
  
enter your response here ​(Simplify your​ answer.)

We are given the function:

\[
f(r) = \sqrt{r + 7} + 9
\]

We need to evaluate this function at the given values of the independent variable.

### a. \( f(-7) \)

Substitute \( r = -7 \) into the function:

\[
f(-7) = \sqrt{-7 + 7} + 9 = \sqrt{0} + 9 = 0 + 9 = 9
\]

Thus, \( f(-7) = 9 \).

Would you like to continue with parts b and c, or need further clarification on part a?

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Here are 5 relative questions:

1. How does changing the constant inside the square root affect the function?
2. What happens if \( r = -8 \) instead of \( r = -7 \)?
3. How would the function change if the square root was squared?
4. Can you graph \( f(r) \) for different values of \( r \)?
5. How does the domain of this function change?

**Tip**: Always check that the expression inside a square root is non-negative when dealing with real numbers.

Evaluate the function f(r) = √(r + 7) + 9 at the given values of the independent variable and simplify. a. f(-7) b. f(9) c. f(x - 7)

Learn how to evaluate the function f(r) = √(r + 7) + 9 at different values of r, including r = -7, r = 9, and r = x - 7. This problem covers key algebraic concepts, such as square roots, substitution, and simplifying expressions. Suitable for students in Grades 8-10.

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