Question

Hey guys if i can get some pointers on how to do this that would be great ive been stuck on this problem for over an hour my notes arent helping me and no one in the household understands it any help would be greatly appreciated.

(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

• a) 3
• b) 6
• c) 9
• d) the outputs are 3 times as far apart as the inputs

Explanation:

(a) "x" in considered to be the input to the function f(x). The variable(s) in parentheses as part of the function name are the inputs. The function value itself is the output.

That is, for an input (x-value) of 0, the output (f(0)) is 5. For an input of 1, the output (f(1)) is 8. These input values (0 and 1) are 1 unit apart: 1 - 0 = 1. The corresponding output values are 3 units apart: 8 - 5 = 3.

(b) Inputs -1 and 1 are 2 units apart (1-(-1)=2). The corresponding output values, 2 and 8, are 6 units apart. (8-2=6)

(c) Inputs 0 and 3 are 3 units apart. The corresponding output values, 5 and 14, are 9 units apart.

(d) The ratio of output differences to input differences can be seen to be ...

... 3/1 = 6/2 = 9/3 = 3

Output differences are 3 times input differences.

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Comment on the problem

These ratios are constant everywhere, so the function is considered to be "linear." The ratio is the "slope" of the line you see when the function is graphed.