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

*f(x)* = −6 + 14*x* 
*g(x)* = (2*x* + 9)2
 


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

Select **TWO** correct answers.



Let's evaluate the functions \( f(x) \) and \( g(x) \) for the given values \( x = 7 \) and \( x = -3 \).

### Function \( f(x) = -6 + 14x \)
Evaluate \( f(7) \):

\[
f(7) = -6 + 14(7)
\]

\[
f(7) = -6 + 98
\]

\[
f(7) = 92
\]

### Function \( g(x) = (2x + 9)^2 \)
Evaluate \( g(-3) \):

\[
g(-3) = (2(-3) + 9)^2
\]

\[
g(-3) = (-6 + 9)^2
\]

\[
g(-3) = 3^2
\]

\[
g(-3) = 9
\]

### Final Answer
The values that Patrick will calculate are:

- \( f(7) = 92 \)
- \( g(-3) = 9 \)

So the correct answers are \( \boxed{92} \) and \( \boxed{9} \).

Would you like more details, or do you have any other questions?

### Relative Questions:
1. How do you evaluate functions for specific values of \( x \)?
2. What is the general form of a linear function?
3. How do you expand and simplify squared binomials like \( (2x + 9)^2 \)?
4. What happens if the input to a function is a fraction or a decimal?
5. Can we evaluate these functions graphically using a graphing calculator?

### Tip:
Always substitute the given value of \( x \) carefully and follow the order of operations (PEMDAS) when evaluating functions.

Practice evaluating functions f(x) = -6 + 14x and g(x) = (2x + 9)^2 for given values of x. Understand the steps involved in function evaluation with detailed examples and solutions. Suitable for Grades 9-10 students learning about functions in algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation