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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

Pergunta

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

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

Solução

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IracemaMestre · Tutor por 5 anos

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### A. 0 < x < 8

Explicação

## 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.
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