The graph in the image shows a straight line on the coordinate plane, and the problem is asking to identify the rate of change of the function, which is the slope of the line.

To find the slope of the line, we use the formula:

$\text{slope (m)} = \frac{{\text{change in y}}}{{\text{change in x}}} = \frac{{y_2 - y_1}}{{x_2 - x_1}}$ We can select two points that the line passes through on the graph. From the image, two clear points on the line are:

• $(0, -3)$
• $(3, 3)$

Now, applying the slope formula: $m = \frac{{3 - (-3)}}{{3 - 0}} = \frac{6}{3} = 2$

Conclusion:

The rate of change of the function is 2.

Would you like further clarification on this? Let me know if you have any questions!

Here are some related questions to explore:

1. What is the equation of the line shown in the graph?
2. How does the slope affect the steepness of a line?
3. What is the slope of a horizontal line and why?
4. Can the slope be negative? If so, what would that mean for the graph?
5. How can you find the y-intercept from the equation of a line?

Tip: The slope tells you how much the y-value changes for every unit of change in the x-value. If the slope is positive, the line rises; if it's negative, the line falls.