https://file.aiquickdraw.com/mathbot/file/1726801474500dku26azy.jpg

Let's analyze and solve the problem in your image.

### Part A: 
The problem asks for the value of \( f(x) = g(x) \) at \( x = 4 \). The graph shows two functions, a red line (likely \( f(x) \)) and a green line (likely \( g(x) \)). At \( x = 4 \), both lines intersect, indicating that \( f(4) = g(4) \). From the graph, we can visually estimate the y-value at the point of intersection, which appears to be around \( y = 0 \).

So:
\[
f(4) = g(4) = 0
\]

### Part B:
1. **\( f(0) \)**: At \( x = 0 \), the red line (representing \( f(x) \)) crosses the y-axis at \( y = 2 \). Therefore:
   \[
   f(0) = 2
   \]

2. **\( g(0) \)**: At \( x = 0 \), the green line (representing \( g(x) \)) crosses the y-axis at approximately \( y = -10 \). Therefore:
   \[
   g(0) = -10
   \]

### True or False Statement:
The problem asks if \( f(0) < g(0) \). We found:
\[
f(0) = 2 \quad \text{and} \quad g(0) = -10
\]
Clearly, \( 2 > -10 \), so the statement \( f(0) < g(0) \) is **false**.

### Summary of Answers:
- Part A: \( f(4) = g(4) = 0 \)
- Part B: \( f(0) = 2 \), \( g(0) = -10 \)
- The statement \( f(0) < g(0) \) is **false**.

Would you like more detailed explanations or have any questions?

### Additional Practice:
1. What is the value of \( f(x) \) when \( x = 2 \)?
2. What is the slope of the function \( f(x) \)?
3. Find where \( f(x) > g(x) \) based on the graph.
4. Can \( f(x) = g(x) \) for another value of \( x \)?
5. What is the equation of the line \( g(x) \)?

**Tip:** Visualizing the intersection points of functions on a graph is a great way to solve equations like \( f(x) = g(x) \).

Determine the intersection point of f(x) and g(x) at x=4, find f(0) and g(0), and verify if the statement f(0) < g(0) is true or false.

In this problem, we solve for the intersection point of two linear functions f(x) and g(x) at x=4, calculate f(0) and g(0), and verify the truth of the inequality f(0) < g(0). Suitable for students in Grades 8-10 learning algebra and function properties.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation