Question

Compare the two functions.
Function 1:
x | -1 | 0 | 1 | 2 | 4 | 5
y | -1 | 3 | 7 | 11 | 19 | 23
Function 2 is attached.
A.) Which function has a larger y-intercept?
B.) Which function has a constant rate of change?
C.) Which function has the greater rate of change in the interval [0,2]?
D.) Which function has the greater rate of change in the interval [2,4]?

Answer 1

To answer the questions, we need to analyze the first function provided and then compare it with the second function.

### Function 1 Details:
- Points: \((-1, -1)\), \((0, 3)\), \((1, 7)\), \((2, 11)\), \((4, 19)\), \((5, 23)\)

#### A.) Which function has a larger y-intercept?
The y-intercept is the value of \(y\) when \(x = 0\).
- For Function 1, the y-intercept is at \(y = 3\) when \(x = 0\).
- For Function 2, we need to check the value of \(y\) at \(x = 0\). Without the values, I cannot determine which is larger.

### Assuming values for Function 2:
To complete this question, we would need the values from Function 2 at \(x=0\).

#### B.) Which function has a constant rate of change?
A function has a constant rate of change if it is linear.
- Function 1 is not linear since the rate of change is not constant:
\[
\text{Rate of change from } 0 \text{ to } 1: \frac{7-3}{1-0} = 4
\]
\[
\text{Rate of change from } 1 \text{ to } 2: \frac{11-7}{2-1} = 4
\]
\[
\text{Rate of change from } 2 \text{ to } 4: \frac{19-11}{4-2} = 4
\]
\[
\text{Rate of change from } 4 \text{ to } 5: \frac{23-19}{5-4} = 4
\]

- Since the rate of change for different intervals comes out to be \(4\), Function 1 does have a constant rate of change.

### Assuming Function 2 is linear or quadratic to answer this question directly; if not, please clarify.

#### C.) Which function has the greater rate of change in the interval [0,2]?
- For Function 1 in the interval [0,2]:
\[
\text{Rate of change} = \frac{11-3}{2-0} = \frac{8}{2} = 4
\]
- For Function 2, the calculation depends on its specific values in that interval.

#### D.) Which function has the greater rate of change in the interval [2,4]?
- For Function 1 in the interval [2,4]:
\[
\text{Rate of change} = \frac{19-11}{4-2} = \frac{8}{2} = 4
\]
- Similarly, the rate of change for Function 2 would need its values.

### Summary:
1. A.) y-intercept — Cannot be determined without Function 2.
2. B.) Function 1 has a constant rate of change (it is linear).
3. C.) Greater rate of change in [0,2] — Depends on Function 2.
4. D.) Greater rate of change in [2,4] — Also depends on Function 2.

Please provide the values for Function 2 for a more accurate comparison!