Patrick is practicing evaluating functions. He is using the following functions.

f(x) = −6 + 14x
g(x) = (2x + 9)2

He evaluates the functions for f(7) and g(−3). What values will he calculate?

Select TWO correct answers.
A.9
B.−28
C.92
D.225
E.104

To solve for the values of \( f(7) \) and \( g(-3) \) using the given functions:

1. **Function \( f(x) = -6 + 14x \)**:
   - Substitute \( x = 7 \) into the function:
   \[
   f(7) = -6 + 14(7) = -6 + 98 = 92
   \]
   So, \( f(7) = 92 \).

2. **Function \( g(x) = (2x + 9)^2 \)**:
   - Substitute \( x = -3 \) into the function:
   \[
   g(-3) = (2(-3) + 9)^2 = (-6 + 9)^2 = (3)^2 = 9
   \]
   So, \( g(-3) = 9 \).

Therefore, the correct answers are:

- **Option A: 9**
- **Option C: 92**

These are the values Patrick will calculate.

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

1. What is the result of \( f(x) = -6 + 14x \) when \( x = 0 \)?
2. How would the function \( g(x) \) change if \( x \) were 2 instead of -3?
3. How do the results change if the coefficient of \( x \) in \( f(x) \) is increased by 2?
4. What is the minimum value of \( g(x) = (2x + 9)^2 \)?
5. How do the graphs of these functions look in comparison to each other?

**Tip:** Always verify your calculations by substituting back into the original function to ensure accuracy.

Learn how to evaluate the functions f(x) = -6 + 14x and g(x) = (2x + 9)^2 for specific values. This problem covers key concepts in function evaluation, including substitution and quadratic functions. Suitable for students in Grades 7-9.

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