The problem is asking for the average rate of change of the function $f(x) = 3x - 5$ and its interpretation in terms of whether the function is increasing or decreasing.

1. Average Rate of Change: The average rate of change for a linear function $f(x) = mx + b$ is simply the slope $m$. In this case, the slope is $3$.

2. Interpretation:

   • When the slope $m > 0$, the function is increasing.
   • When the slope $m < 0$, the function is decreasing.

For $f(x) = 3x - 5$, the slope is $3$, which is positive, meaning the function is increasing.

Therefore, the correct answer is:

• "The average rate of change is 3, and the function is increasing."

The selection in the image is incorrect, as it says the function is decreasing.

Would you like more details on how we calculated the rate of change?

5 Related Questions:

1. What is the rate of change of the function $f(x) = -2x + 4$?
2. How does the rate of change affect whether a function is increasing or decreasing?
3. Can the rate of change for a quadratic function be constant?
4. What is the average rate of change of $f(x) = x^2$ between $x = 1$ and $x = 3$?
5. How can you interpret the slope of a linear function in real-world contexts?

Tip:

For any linear function $f(x) = mx + b$, the slope $m$ always tells you the constant rate of change, making calculations very straightforward.