Question

Question

Function A:
Graph points: (-4,0) , (-2,1) , (0,2) , (2,3)

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 determine the answers to the questions, we will analyze each function based on the given information.

Function A: The points given are (-4,0), (-2,1), (0,2), (2,3). We can calculate the slope (rate of change) between the points:

1. From (-4,0) to (-2,1): \[ \text{Slope} = \frac{1 - 0}{-2 - (-4)} = \frac{1}{2} \]
2. From (-2,1) to (0,2): \[ \text{Slope} = \frac{2 - 1}{0 - (-2)} = \frac{1}{2} \]
3. From (0,2) to (2,3): \[ \text{Slope} = \frac{3 - 2}{2 - 0} = \frac{1}{2} \]

The rate of change (slope) for Function A is positive (1/2).

Function B: Given points are (0,3), (4,-9), (8,-21). Calculate the slope between the points:

1. From (0,3) to (4,-9): \[ \text{Slope} = \frac{-9 - 3}{4 - 0} = \frac{-12}{4} = -3 \]
2. From (4,-9) to (8,-21): \[ \text{Slope} = \frac{-21 - (-9)}{8 - 4} = \frac{-12}{4} = -3 \]

The rate of change (slope) for Function B is negative (-3).

Function C: The equation is \( y = x + 5 \). Here, the slope is 1 (positive).

Answers to the Questions:

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

   • Function B has a negative rate of change.

2. Which function has the smallest y-intercept?

   • For Function A, the y-intercept is 2 (when x=0).
   • For Function B, the y-intercept is 3 (when x=0).
   • For Function C, the y-intercept is 5 (when x=0).
   • Function A has the smallest y-intercept (2).

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

   • A function with a positive slope (rate of change) is preferable for representing income.
   • Function A or Function C could represent money earned per hour, but since Function A has a stronger upward trend (from 0 to 3), it might be more representative than C, which grows linearly. Thus, Function A is the better choice.

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

   • Looking at the y-intercepts again:
     • Function A gives 2 at x=0.
     • Function B gives 3 at x=0.
     • Function C gives 5 at x=0.
   • Function C gives the highest initial amount of money (5).

In summary:

1. Function B
2. Function A
3. Function A
4. Function C