Question

Select the correct statement about the function represented by the table.
X | Y
1. | 26
2. | 44
3. | 62
4. | 80
5. | 98
It is an exponential function because the y values increase by an equal factor over equal intervals of x values.
B. It is an exponential function because the factor between each x-and y-value is constant.
C. I1 is a linear function because the y values increase by an equal difference over equal intervals of x-values.
D. Il is a linear function because the difference y = x for each row is
constant.

Answer 1

To analyze the function represented by the table provided, we need to determine if the relationship between the x and y values is linear or exponential.

The table is:

```
X | Y
1 | 26
2 | 44
3 | 62
4 | 80
5 | 98
```

Now, let's calculate the differences in y values as x increases:

- From x=1 to x=2: \(44 - 26 = 18\)
- From x=2 to x=3: \(62 - 44 = 18\)
- From x=3 to x=4: \(80 - 62 = 18\)
- From x=4 to x=5: \(98 - 80 = 18\)

Since the differences between consecutive y values are constant (18), this indicates that the relationship is linear.

Now, let's check the statement options:

A. **It is an exponential function...** - This is incorrect because the y-values do not increase by an equal factor.

B. **It is an exponential function...** - This is also incorrect since the relationship is linear, not exponential.

C. **It is a linear function because the y values increase by an equal difference over equal intervals of x-values.** - This is a correct statement based on our analysis.

D. **It is a linear function because the difference y = x for each row is constant.** - This statement is phrased incorrectly. The constant difference is in y values, not simply equating \(y\) to \(x\).

Thus, the correct answer is **C**: It is a linear function because the y values increase by an equal difference over equal intervals of x-values.