https://file.aiquickdraw.com/mathbot/file/1724876312793ojh63erx.jpg

To find the equation of \( g(x) \), let's analyze the graph in the image provided. 

1. **Identifying \( f(x) \) and \( g(x) \) on the Graph:**
   - The graph shows two functions: \( f(x) = \sqrt{x} \) in black, which is a square root function, and \( g(x) \) in blue, which appears to be a line.

2. **Analyzing \( g(x) \):**
   - \( g(x) \) is a straight line, which suggests that its equation is of the form \( g(x) = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

3. **Finding the Slope (\( m \)):**
   - To determine the slope, identify two points on the line \( g(x) \). For example, it looks like the line passes through the points \((0, 3)\) and \((10, 0)\).
   - Slope formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \)
   - Substituting the points: \( m = \frac{0 - 3}{10 - 0} = \frac{-3}{10} = -0.3 \).

4. **Finding the Y-intercept (\( b \)):**
   - From the graph, the y-intercept \( b \) is approximately 3 because \( g(x) \) crosses the y-axis at \( y = 3 \).

5. **Equation of \( g(x) \):**
   - Using the slope-intercept form, \( g(x) = mx + b \):
   - \( g(x) = -0.3x + 3 \).

Thus, the equation for \( g(x) \) is:

\[
g(x) = -0.3x + 3
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you determine the slope of a line from a graph?
2. What is the significance of the y-intercept in the equation of a line?
3. How do you graph a square root function like \( f(x) = \sqrt{x} \)?
4. Can two different functions intersect at more than one point?
5. How do transformations affect the graph of a function?

### Tip:
To find the equation of a line, always look for clear points where the line crosses grid lines. These points make it easier to calculate the slope and y-intercept accurately.

Learn how to find the equation of g(x) from a graph with a detailed step-by-step analysis. Understand the concepts of graphing functions and linear equations using examples. Suitable for high school students studying algebra and graphing functions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation