Question

Determine whether the following table represents a linear or an exponential function. Explain why or why not.
x
0
1
2
3
y
7
9
11
13
Question content area bottom
Part 1
Does the table represent a linear or an exponential​ function? Why or why​ not?
A.
​Exponential; all of the​ x-values have a common difference and all of the​ y-values have a common ratio.
B.
​Linear; all of the​ x-values have a common difference and all of the​ y-values have a common difference.
C.
​Exponential; all of the​ x-values have a common ratio and all of the​ y-values do not have a common difference.
D.
​Linear; all of the​ x-values have a common difference and all of the​ y-values have a common ratio.

Answer 1

To determine whether the given table represents a linear or an exponential function, we need to analyze the differences in the x-values and y-values.

**Table:**
```
x: 0, 1, 2, 3
y: 7, 9, 11, 13
```

1. **Identify the common differences:**
- The x-values increase by a constant amount of 1 (common difference of 1).
- For the y-values:
- From 7 to 9: increase of 2
- From 9 to 11: increase of 2
- From 11 to 13: increase of 2
- The difference between consecutive y-values is consistent (also a common difference of 2).

2. **Determine the function type:**
- A function is **linear** if the differences between the y-values are constant for equal increments in x (which has been observed here).
- A function is **exponential** if the ratios of the y-values for equal increments in x are constant, but that is not the case here.

From the analysis above, we see that:
- All of the x-values have a common difference (1).
- All of the y-values have a common difference (2).

Therefore, the correct choice is:

**B. Linear; all of the x-values have a common difference and all of the y-values have a common difference.**