https://file.aiquickdraw.com/mathbot/file/1726290650277ghtd6l8v.jpg

Use the graphs of 𝑓
 and 𝑔
 to find and simplify the indicated values.

 Click on the graph to view the enlarged graph

(𝑓+𝑔)(3)=
 
functionsequation editor
(𝑔−𝑓)(−2)=
 
functionsequation editor
(𝑓𝑔)(5)=
 
functionsequation editor
(𝑔𝑓)(−4)=
 

To solve the given problems using the provided graph of the functions \( f(x) \) and \( g(x) \), let's break down each expression:

### 1. \( (f + g)(3) \)
This is asking for the sum of the values of \( f(x) \) and \( g(x) \) when \( x = 3 \).

- From the graph, \( f(3) \) is the red point at \( x = 3 \), which corresponds to the value 2.
- Similarly, \( g(3) \) is the blue point at \( x = 3 \), which corresponds to the value -3.

Thus, \( (f + g)(3) = f(3) + g(3) = 2 + (-3) = -1 \).

### 2. \( (g - f)(-2) \)
This is asking for the difference between the values of \( g(x) \) and \( f(x) \) when \( x = -2 \).

- From the graph, \( g(-2) \) is the blue point at \( x = -2 \), which corresponds to the value 2.
- \( f(-2) \) is the red point at \( x = -2 \), which corresponds to the value 3.

Thus, \( (g - f)(-2) = g(-2) - f(-2) = 2 - 3 = -1 \).

### 3. \( (f \cdot g)(5) \)
This is asking for the product of the values of \( f(x) \) and \( g(x) \) when \( x = 5 \).

- From the graph, \( f(5) \) is the red point at \( x = 5 \), which corresponds to the value -2.
- \( g(5) \) is the blue point at \( x = 5 \), which corresponds to the value -4.

Thus, \( (f \cdot g)(5) = f(5) \cdot g(5) = (-2) \cdot (-4) = 8 \).

### 4. \( (g \cdot f)(-4) \)
This is asking for the product of the values of \( g(x) \) and \( f(x) \) when \( x = -4 \).

- From the graph, \( g(-4) \) is the blue point at \( x = -4 \), which corresponds to the value -3.
- \( f(-4) \) is the red point at \( x = -4 \), which corresponds to the value 4.

Thus, \( (g \cdot f)(-4) = g(-4) \cdot f(-4) = (-3) \cdot 4 = -12 \).

### Summary of results:
1. \( (f + g)(3) = -1 \)
2. \( (g - f)(-2) = -1 \)
3. \( (f \cdot g)(5) = 8 \)
4. \( (g \cdot f)(-4) = -12 \)

Would you like more details or have any other questions?

Here are 5 relative questions to deepen understanding:
1. What is the value of \( (f + g)(-1) \)?
2. How do you interpret the intersection point of \( f(x) \) and \( g(x) \)?
3. Can you find \( (g \cdot f)(1) \)?
4. What happens when \( (f - g)(0) \)?
5. How would you calculate \( f(4) + g(4) \)?

**Tip:** Always check both the function's x-coordinate and y-coordinate values carefully before solving function-related problems from graphs.

Use the graphs of f(x) and g(x) to find and simplify the indicated values: (f+g)(3), (g-f)(-2), (f*g)(5), (g*f)(-4).

Learn how to perform addition, subtraction, and multiplication of functions using graphs. This example uses two functions, f(x) and g(x), to solve (f+g)(3), (g-f)(-2), (f*g)(5), and (g*f)(-4). Suitable for Grades 9-11 students studying algebraic function operations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation