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 hours on Saturdays. Here:- : Represents the hourly earnings (\$14 per hour multiplied by the number of hours worked).- : Represents the base pay Eve receives regardless of hours worked.## Step 2: Analyze the table data### From the table, we observe that:- For , \( f(1) = 26 \).- For , \( f(2) = 40 \).- For , \( f(3) = 54 \).- For , \( f(4) = 68 \).- For , \( f(5) = 82 \).This confirms that the function \( f(x) = 14x + 12 \) accurately models the relationship between hours worked ( ) and total pay (\( f(x) \)).## Step 3: Determine the reasonable domain### The domain of a function refers to the set of possible input values ( ) for which the function is defined. In this case:- 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 .Other options, such as , , or , 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.