On Saturdays, Eve earns 14 per hour for yard work and an extra amount for dog walking. Hours & 1 & 2 & 3 & 4 & 5 Pay & 26 & 40 & 54 & 68 & 82 Which is a reasonable domain for the function f(x)=14 x+12 ? A. 0<x<8 B. 0<x<24 C. 26<x<82 D. 0<x<82

## Step 1: Understand the function and its components
### The function $f(x) = 14x + 12$ represents Eve's total pay for working $x$ hours on Saturdays. Here:
- $14x$: Represents the hourly earnings ($14 per hour multiplied by the number of hours worked).
- $12$: Represents the base pay Eve receives regardless of hours worked.

## Step 2: Analyze the table data
### From the table, we observe that:
- For $x = 1$, $f(1) = 26$.
- For $x = 2$, $f(2) = 40$.
- For $x = 3$, $f(3) = 54$.
- For $x = 4$, $f(4) = 68$.
- For $x = 5$, $f(5) = 82$.

This confirms that the function $f(x) = 14x + 12$ accurately models the relationship between hours worked ($x$) and total pay ($f(x)$).

## Step 3: Determine the reasonable domain
### The domain of a function refers to the set of possible input values ($x$) for which the function is defined. In this case:
- $x$ represents the number of hours worked.
- Since Eve works between 0 and 8 hours on Saturdays (as implied by the context), the reasonable domain is $0 < x < 8$.

Other options, such as $0 < x < 24$, $26 < x < 82$, or $0 < x < 82$, are not reasonable because they either exceed the maximum hours Eve can work or incorrectly describe the range of pay instead of the domain of hours worked.