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consider the table below:
Input -2 1 4 7 10 13
output 15 13 11 9 7 5
a. does the table below represent a function?
b.write an equation that will generate the output from the input
c.find the output when the input is -7
d. find the input when the output is -25

Sagot :

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