1. Let
![x](https://tex.z-dn.net/?f=x)
be the number of hours that you worked. We know from our problem that your hourly wage is $8, so your hourly wage will be given by the linear function:
![y=8x](https://tex.z-dn.net/?f=y%3D8x)
.
where
![f(x)](https://tex.z-dn.net/?f=f%28x%29)
is your gross pay.
![x](https://tex.z-dn.net/?f=x)
is the number of hours that you worked.
To complete the table, we just need to evaluate the function at the given hours; in other words, we are going to replace
![x](https://tex.z-dn.net/?f=x)
with the number of hours in our linear function:
![y=8(0)=0](https://tex.z-dn.net/?f=y%3D8%280%29%3D0)
![y=8(3)=24](https://tex.z-dn.net/?f=y%3D8%283%29%3D24)
![y=8(5)=40](https://tex.z-dn.net/?f=y%3D8%285%29%3D40)
![y=8(7)=56](https://tex.z-dn.net/?f=y%3D8%287%29%3D56)
![y=8(10)=80](https://tex.z-dn.net/?f=y%3D8%2810%29%3D80)
![y=8(12)=96](https://tex.z-dn.net/?f=y%3D8%2812%29%3D96)
We can conclude that yous should fill your table as follows:
<span>
Number of Hours03571012
</span><span>
Gross Pay
0
24
40
56
80
96
2. Remember that the domain of a function are the set of the x-values of the function; the range of a function are the set of y-values of the function. From our previous point, we can infer that the ordered pairs of the function are: (0,0), (3,24), (5,40), (7,56), (10,80), and (12,96). The y-values and hence the range of the function are: 0, 24, 40, 56, 80, 96. Remember that in the quadrant I both the
x-coordinates and the
y-coordinates are
positive. Since all the coordinates of our points are positive, we can conclude that the correct answer is:
</span><span>
d. 0, 24, 40, 56, 80, 96; Quadrant I</span>