Given:
x: -5 -4 -3 -2 -1 0 1 2 3
f(x): -20 -13 -6 1 8 15 22 29 36
The set of x values are the input values
The set of f(x) values are the output values
a) Let's take the the values for -5 and -4 since all each x value is 1 unit apart from the next x value.
Thus the difference is:
f(-4) - f(-5) = -13 - (-20)
= -13 + 20
= 7
b) Inputs that are 2 units apart:
-3 - (-5) = -3 + 5 = 2
Since they are 2 units apart, let's find the difference between f(-3) and f(-5):
f(-3) - f(-5) = -6 - (-20)
= -6 + 20
= 14
c) Inputs that are 3 units apart:
3 - 0 = 3
Since they are 3 units apart, find the diffference between f(3) - f(0):
f(3) - f(0) = 36 - 15
= 21
d) Differnce in output : Differnce in input = -13 - (-20) : -4 -(-5)
= 7 : 1
As the input increases by 1 unit, the output also increases by 7 units.
The ratio of the differences in output to input intervals is = 7:1
ANSWER:
a) 7
b) 14
c) 21
d) 7:1