Question
Select all of the statements that are true about the functions below:
Choose ALL answers that apply
Function A is an exponential function that passes through (8, 0), (0, 1), and (-2, 4). Function B is a table with the following information.
x|-7|-6|-5|-4|-3
y|1.5|3|4.5|6|7.5
(1 point)
Responses
Function A is Linear
Function A is Linear
The rate of change of Function A is always 1/2
The rate of change of Function A is always 1/2
The value of Function B increaes by 1.5 when the value of xz increases by 1
The value of Function B increaes by 1.5 when the value of xz increases by 1
The rate of change of Function B is Always 1.5.
The rate of change of Function B is Always 1.5.
Function B is linear
Function B is linear
Function B has constant growth factor of 1.5
Choose ALL answers that apply
Function A is an exponential function that passes through (8, 0), (0, 1), and (-2, 4). Function B is a table with the following information.
x|-7|-6|-5|-4|-3
y|1.5|3|4.5|6|7.5
(1 point)
Responses
Function A is Linear
Function A is Linear
The rate of change of Function A is always 1/2
The rate of change of Function A is always 1/2
The value of Function B increaes by 1.5 when the value of xz increases by 1
The value of Function B increaes by 1.5 when the value of xz increases by 1
The rate of change of Function B is Always 1.5.
The rate of change of Function B is Always 1.5.
Function B is linear
Function B is linear
Function B has constant growth factor of 1.5
Answers
GPT-4o mini
Let's analyze the statements based on the information provided:
1. **Function A is Linear**
- **False**: You mentioned that Function A is an exponential function. Therefore, it is not linear.
2. **The rate of change of Function A is always 1/2**
- **False**: As Function A is exponential, its rate of change is not constant. In exponential functions, the rate of change increases or decreases as x changes.
3. **The value of Function B increases by 1.5 when the value of x increases by 1**
- **True**: Checking the table for Function B:
- From -7 to -6: y goes from 1.5 to 3 (increase of 1.5)
- From -6 to -5: y goes from 3 to 4.5 (increase of 1.5)
- From -5 to -4: y goes from 4.5 to 6 (increase of 1.5)
- From -4 to -3: y goes from 6 to 7.5 (increase of 1.5)
- Therefore, the value does consistently increase by 1.5.
4. **The rate of change of Function B is Always 1.5**
- **True**: As shown above, the difference in y-values is consistently 1.5 for each unit increase in x.
5. **Function B is linear**
- **True**: Since the rate of change is constant (1.5), Function B can be described as linear.
6. **Function B has a constant growth factor of 1.5**
- **False**: While the increase in y is constant (1.5), a constant growth factor typically refers to a multiplicative change, which is not applicable here since we have additive changes.
Based on this analysis, the **true statements** are:
- The value of Function B increases by 1.5 when the value of x increases by 1.
- The rate of change of Function B is Always 1.5.
- Function B is linear.
1. **Function A is Linear**
- **False**: You mentioned that Function A is an exponential function. Therefore, it is not linear.
2. **The rate of change of Function A is always 1/2**
- **False**: As Function A is exponential, its rate of change is not constant. In exponential functions, the rate of change increases or decreases as x changes.
3. **The value of Function B increases by 1.5 when the value of x increases by 1**
- **True**: Checking the table for Function B:
- From -7 to -6: y goes from 1.5 to 3 (increase of 1.5)
- From -6 to -5: y goes from 3 to 4.5 (increase of 1.5)
- From -5 to -4: y goes from 4.5 to 6 (increase of 1.5)
- From -4 to -3: y goes from 6 to 7.5 (increase of 1.5)
- Therefore, the value does consistently increase by 1.5.
4. **The rate of change of Function B is Always 1.5**
- **True**: As shown above, the difference in y-values is consistently 1.5 for each unit increase in x.
5. **Function B is linear**
- **True**: Since the rate of change is constant (1.5), Function B can be described as linear.
6. **Function B has a constant growth factor of 1.5**
- **False**: While the increase in y is constant (1.5), a constant growth factor typically refers to a multiplicative change, which is not applicable here since we have additive changes.
Based on this analysis, the **true statements** are:
- The value of Function B increases by 1.5 when the value of x increases by 1.
- The rate of change of Function B is Always 1.5.
- Function B is linear.