Question

1.     The table shows a linear function.
x
-5
-4
-3
-2
-1
0
1
2
3
----------------------
f (x)
-11
-5
3
13
21
29
37
45
53
 
(a)   Determine the difference of outputs of any two inputs that are 1 unit apart. Show your work.
(b)   Determine the difference of outputs of any two inputs that are 2 units apart. Show your work.
(c)   Determine the difference of outputs of any two inputs that are 3 units apart. Show your work.
(d)   What do you notice about the ratios of the differences in the outputs to the input intervals? Explain your answer.

Answer 1

Answer:

a) I used the equation x=-5; f(x)=-11 and x=-4; f(x)=-3. We get the range = -3-(-11)=8

b) I used the equation x=-5; f(x)=-11 and x=-3; f(x)=5. We get the range = 5-(-11)=16

c) I used the equation x=-5; f(x)=-11 and x=-2; f(x)=13. We get the range = 13-(-11)=24

d) Range of input is equal with the ratios of the output. You can find the pattern of output above 8,16,and 24 can divided by 8 and give the result 1,2 and 3