Question
Compare the two functions.
Function 1:
x 0 1 2 3 4 5
y -1 3 7 11 15 19
Function 2:
exponential graph (5,28) (4,12) (2,0) (0,-3)
(2 points)
Which function has the lower y-intercept?
Which function has a constant rate of change?
Function 1:
x 0 1 2 3 4 5
y -1 3 7 11 15 19
Function 2:
exponential graph (5,28) (4,12) (2,0) (0,-3)
(2 points)
Which function has the lower y-intercept?
Which function has a constant rate of change?
Answers
GPT-4o mini
To compare the two functions, we first need to analyze their properties based on the given points.
### Function 1:
The values for Function 1 are:
- \(x = 0 \Rightarrow y = -1\)
- \(x = 1 \Rightarrow y = 3\)
- \(x = 2 \Rightarrow y = 7\)
- \(x = 3 \Rightarrow y = 11\)
- \(x = 4 \Rightarrow y = 15\)
- \(x = 5 \Rightarrow y = 19\)
**Y-Intercept:** The y-intercept is the value of \(y\) when \(x = 0\). For Function 1, the y-intercept is \(-1\).
**Constant Rate of Change:** To determine if Function 1 has a constant rate of change, we can calculate the differences in \(y\) values for consecutive \(x\) values:
- From \(0\) to \(1\) : \(3 - (-1) = 4\)
- From \(1\) to \(2\) : \(7 - 3 = 4\)
- From \(2\) to \(3\) : \(11 - 7 = 4\)
- From \(3\) to \(4\) : \(15 - 11 = 4\)
- From \(4\) to \(5\) : \(19 - 15 = 4\)
Since the rate of change is consistent (\(4\)), Function 1 has a constant rate of change.
### Function 2:
Function 2 is represented by points on an exponential graph. The given points are:
- (5, 28)
- (4, 12)
- (2, 0)
- (0, -3)
**Y-Intercept:** The y-intercept is the value of \(y\) when \(x = 0\). For Function 2, the y-intercept is \(-3\).
**Constant Rate of Change:** To assess if Function 2 has a constant rate of change, we should analyze the change in \(y\) values between the points:
- From \(0\) to \(2\) : \(0 - (-3) = 3\)
- From \(2\) to \(4\) : \(12 - 0 = 12\)
- From \(4\) to \(5\) : \(28 - 12 = 16\)
The differences in \(y\) values are not consistent; hence, Function 2 does not have a constant rate of change.
### Summary:
1. **Which function has the lower y-intercept?**
- Function 2 has the lower y-intercept (-3) compared to Function 1 (-1).
2. **Which function has a constant rate of change?**
- Function 1 has a constant rate of change. Function 2 does not.
### Function 1:
The values for Function 1 are:
- \(x = 0 \Rightarrow y = -1\)
- \(x = 1 \Rightarrow y = 3\)
- \(x = 2 \Rightarrow y = 7\)
- \(x = 3 \Rightarrow y = 11\)
- \(x = 4 \Rightarrow y = 15\)
- \(x = 5 \Rightarrow y = 19\)
**Y-Intercept:** The y-intercept is the value of \(y\) when \(x = 0\). For Function 1, the y-intercept is \(-1\).
**Constant Rate of Change:** To determine if Function 1 has a constant rate of change, we can calculate the differences in \(y\) values for consecutive \(x\) values:
- From \(0\) to \(1\) : \(3 - (-1) = 4\)
- From \(1\) to \(2\) : \(7 - 3 = 4\)
- From \(2\) to \(3\) : \(11 - 7 = 4\)
- From \(3\) to \(4\) : \(15 - 11 = 4\)
- From \(4\) to \(5\) : \(19 - 15 = 4\)
Since the rate of change is consistent (\(4\)), Function 1 has a constant rate of change.
### Function 2:
Function 2 is represented by points on an exponential graph. The given points are:
- (5, 28)
- (4, 12)
- (2, 0)
- (0, -3)
**Y-Intercept:** The y-intercept is the value of \(y\) when \(x = 0\). For Function 2, the y-intercept is \(-3\).
**Constant Rate of Change:** To assess if Function 2 has a constant rate of change, we should analyze the change in \(y\) values between the points:
- From \(0\) to \(2\) : \(0 - (-3) = 3\)
- From \(2\) to \(4\) : \(12 - 0 = 12\)
- From \(4\) to \(5\) : \(28 - 12 = 16\)
The differences in \(y\) values are not consistent; hence, Function 2 does not have a constant rate of change.
### Summary:
1. **Which function has the lower y-intercept?**
- Function 2 has the lower y-intercept (-3) compared to Function 1 (-1).
2. **Which function has a constant rate of change?**
- Function 1 has a constant rate of change. Function 2 does not.