1. Let [tex]x[/tex] 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: [tex]y=8x[/tex].
where
[tex]f(x)[/tex] is your gross pay.
[tex]x[/tex] 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 [tex]x[/tex] with the number of hours in our linear function:
[tex]y=8(0)=0[/tex]
[tex]y=8(3)=24[/tex]
[tex]y=8(5)=40[/tex]
[tex]y=8(7)=56[/tex]
[tex]y=8(10)=80[/tex]
[tex]y=8(12)=96[/tex]
We can conclude that yous should fill your table as follows:
Number of Hours
0
3
5
7
10
12
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:
d. 0, 24, 40, 56, 80, 96; Quadrant I
