Question

Question
Function A:

\begin{tikzpicture}[scale=0.5]
\begin{axis}[xmin=-6,xmax=6,ymin=-6,ymax=6, axis lines=middle]
\addplot[mark=*] coordinates{(-4,-1)(-2,1)(0,3)(2,5)};
\end{axis}
\end{tikzpicture}

Function B:

x y
0 3
4 -9
8 -21
Function C: y=x+5

(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 functions given in the question:

1. **Function A:** Points are (-4, -1), (-2, 1), (0, 3), (2, 5). The slope can be determined between the points and is positive as y increases as x increases.

2. **Function B:** The points provided are (0, 3), (4, -9), and (8, -21). To find the slope between (0, 3) and (4, -9):
\[
\text{slope} = \frac{-9 - 3}{4 - 0} = \frac{-12}{4} = -3
\]
The slope is negative. Similarly, between (4, -9) and (8, -21):
\[
\text{slope} = \frac{-21 - (-9)}{8 - 4} = \frac{-12}{4} = -3
\]
The slope is also negative here.

3. **Function C:** The equation is \( y = x + 5 \), which has a slope of 1 (positive).

Now, let's answer the questions:

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

2. **Which function has the smallest y-intercept?**
The y-intercepts are:
- Function A: The point at \( x = 0 \) is (0, 3) → y-intercept = 3
- Function B: The point at \( x = 0 \) is (0, 3) → y-intercept = 3
- Function C: The y-intercept is when \( x = 0 \) → \( y = 0 + 5 = 5 \) → y-intercept = 5
All functions have the same y-intercept at (0, 3) and thus the smallest y-intercept is **3** for Functions A and B.

3. **Which function would you want to represent your money earned per hour?**
**Function A** is the most reasonable to represent money earned per hour because it has a positive slope, which indicates money is increasing.

4. **Which function would give you the highest initial amount of money?**
The y-intercept of each function indicates the initial amount of money. Since all functions A and B have the same initial amount of 3 and function C has an initial value of 5, we conclude that **Function C** gives the highest initial amount of money (5).

### Summary of Answers:
1. **Negative rate of change:** Function B
2. **Smallest y-intercept:** 3 (Functions A and B)
3. **Money earned per hour:** Function A
4. **Highest initial amount of money:** Function C (5)