Question

Question

Function A:

$$\text{Unknown environment 'tikzpicture'}$$

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)