Asked by BTS ARMY
function A is a straight line Function B: Function C: y=x+5
that is plotted at (-4, 0) x y
(-2, 1) (0, 2) 0 3
(2, 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?
that is plotted at (-4, 0) x y
(-2, 1) (0, 2) 0 3
(2, 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?
Answers
Answered by
BTS ARMY
2nd question is function A the rest are correct.
Answered by
GPT-4o mini
To analyze the given functions, we can start by considering the pattern and characteristics of each function, based on the provided information.
1. **Function A**: Plotted points at (-4, 0), (-2, 1), and (2, 3) indicate it is a straight line. To determine its slope, we can use the change in y over the change in x (rise/run). Between the points (-4, 0) and (2, 3):
- Change in y = 3 - 0 = 3
- Change in x = 2 - (-4) = 6
- Slope (m) = Change in y / Change in x = 3 / 6 = 1/2 (positive slope).
2. **Function B**: It is a table of values:
```
x | y
------
0 | 3
4 | -9
8 | -21
```
Looking at the values:
- From 0 to 4: y goes from 3 to -9 (decreases of 12 in y)
- From 4 to 8: y goes from -9 to -21 (decreases by 12 again)
The rate of change is negative as y decreases when x increases, suggesting a negative slope.
3. **Function C**: Represented by the equation \(y = x + 5\).
- The slope is 1 (positive) since the coefficient of x is positive.
- The y-intercept is 5 (when x = 0, y = 5).
Now we can answer the specific 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?**
- The y-intercepts are as follows:
- Function A has no clear y-intercept from the points directly because we don’t have an explicit equation.
- Function B appears to have points well below 0 for x values greater than 0.
- Function C has a y-intercept of 5.
- Thus, Function B has the smallest y-intercept (which is less than 0).
3. **Which function would you want to represent your money earned per hour?**
- You would want a function with a positive slope. Thus, **Function C** (y = x + 5) would be the most suitable choice as it indicates that money earned increases with each hour worked.
4. **Which function would give you the highest initial amount of money?**
- The highest initial amount of money refers to the y-intercept when x = 0.
- Function C has a y-intercept of 5, and Function B has values that start below 0.
- Therefore, **Function C** would give you the highest initial amount of money.
In summary:
- Function with negative rate of change: **Function B**
- Function with the smallest y-intercept: **Function B**
- Function to represent money earned per hour: **Function C**
- Function with the highest initial amount of money: **Function C**
1. **Function A**: Plotted points at (-4, 0), (-2, 1), and (2, 3) indicate it is a straight line. To determine its slope, we can use the change in y over the change in x (rise/run). Between the points (-4, 0) and (2, 3):
- Change in y = 3 - 0 = 3
- Change in x = 2 - (-4) = 6
- Slope (m) = Change in y / Change in x = 3 / 6 = 1/2 (positive slope).
2. **Function B**: It is a table of values:
```
x | y
------
0 | 3
4 | -9
8 | -21
```
Looking at the values:
- From 0 to 4: y goes from 3 to -9 (decreases of 12 in y)
- From 4 to 8: y goes from -9 to -21 (decreases by 12 again)
The rate of change is negative as y decreases when x increases, suggesting a negative slope.
3. **Function C**: Represented by the equation \(y = x + 5\).
- The slope is 1 (positive) since the coefficient of x is positive.
- The y-intercept is 5 (when x = 0, y = 5).
Now we can answer the specific 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?**
- The y-intercepts are as follows:
- Function A has no clear y-intercept from the points directly because we don’t have an explicit equation.
- Function B appears to have points well below 0 for x values greater than 0.
- Function C has a y-intercept of 5.
- Thus, Function B has the smallest y-intercept (which is less than 0).
3. **Which function would you want to represent your money earned per hour?**
- You would want a function with a positive slope. Thus, **Function C** (y = x + 5) would be the most suitable choice as it indicates that money earned increases with each hour worked.
4. **Which function would give you the highest initial amount of money?**
- The highest initial amount of money refers to the y-intercept when x = 0.
- Function C has a y-intercept of 5, and Function B has values that start below 0.
- Therefore, **Function C** would give you the highest initial amount of money.
In summary:
- Function with negative rate of change: **Function B**
- Function with the smallest y-intercept: **Function B**
- Function to represent money earned per hour: **Function C**
- Function with the highest initial amount of money: **Function C**