a. It represents a function because of one to one relationship. The values in iput are the x-values, the domain. The values is out are the y-values, the range which values are depended on x.
x: -2, 1, 4, 7, 10, 13
y: 15, 13, 11, 9, 7, 5
b. You can use the slope-point formula:
y-y1 = y2-y1 (x-x1)
x2-x1
Let's take the 2 pairs of point (x,y)
(-2, 15) (1,13)
x1 = -2 x2 = 1 y1 = 15 y2 = 13
y - 15 = 13 - 15 (x - -2)
1 - - 2
y - 15 = -2 (x + 2)
1+3
y-15 = -2/3 (x + 2)
y - 15 = -2x/3 - 4/3
y = - 2x/3 - 4/3 + 15
y = -2x/3 - 4/3 + 45/3
y = -2x/3 + 41/3
The function is linear:
f(x) = -2x/3 + 41/3
3. Using the the equation for input = -7
f (-7) = -2(-7) + 41/3
3
f(-7) = 14/3 + 41/3
f(-7) = 54/3
f(-7) = 18
input: -7, output = 18
4. output = -25, input = ?
-25 = -2/3x + 41/3
2/3x = 41/3 + 25
2/3 x = 41/3 + 75/3
2/3x = 116/3
(3/2) (2/3)x = (116/3) (3/2)
x = 58
Input= 58, output = -25