Question

Function B: Function C: y=x+5
x y
0 3
4 -9
8 -21
(4 points)
Which function has a negative rate of change (slope)?

Which function has the smallest y-intercept?

Which function would you want to represent your money earned per hour?

Which function would give you the highest initial amount of money?

Answer 1

To analyze the two functions, let’s first determine the equations represented by the points provided.

Function B: Points given are (0, 3), (4, -9), (8, -21). We can calculate the slope (rate of change) using the formula:

\[
\text{slope} = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's use points (0, 3) and (4, -9):

\[
\text{slope} = \frac{-9 - 3}{4 - 0} = \frac{-12}{4} = -3
\]

Now let’s find the slope between (4, -9) and (8, -21):

\[
\text{slope} = \frac{-21 - (-9)}{8 - 4} = \frac{-21 + 9}{4} = \frac{-12}{4} = -3
\]

So, Function B has a negative slope (-3), indicating it has a negative rate of change.

Now let's look at Function C, which is given as \(y = x + 5\). The slope here is 1 (positive).

**1.** Which function has a negative rate of change (slope)?
- **Function B** has a negative rate of change (slope of -3).

**2.** Which function has the smallest y-intercept?
- The y-intercept of Function B (when \(x = 0\)) is \(y = 3\).
- The y-intercept of Function C (when \(x = 0\)) is \(y = 5\).
- **Function B** has the smallest y-intercept (3).

**3.** Which function would you want to represent your money earned per hour?
- You would want a function with a positive slope to represent money earned per hour. Since **Function C** has a positive slope (1), it is more appropriate for this context.

**4.** Which function would give you the highest initial amount of money?
- The initial amount of money corresponds to the y-intercept. As calculated, Function B has a y-intercept of 3, and Function C has a y-intercept of 5.
- Therefore, **Function C** would give you the highest initial amount of money (5).

**Summary:**
1. Function B has a negative rate of change.
2. Function B has the smallest y-intercept.
3. Function C is better for representing money earned per hour.
4. Function C gives the highest initial amount of money.