Question

Can get some help on this question please?

Answer 1

Step-by-step explanation:

The input is x on the first row

The output is f(x) on the second row

a) to determine the difference of outputs of any two inputs that are 1 unit apart, let us take x = -4 and x = -5

The outputs at these inputs are -3 and - 11 respectively

Difference in output = - 3 - - 11 = 8

b) to determine the difference of outputs of any two inputs that are 2 units apart, let us take x = -3 and x = -5

The outputs at these inputs are 5 and - 11 respectively

Difference in output = 5 - - 11 = 16

c)to determine the difference of outputs of any two inputs that are 3 units apart, let us take x = -2 and x = -5

The outputs at these inputs are 13 and - 11 respectively

Difference in output = 13 - - 11 = 24

d) as the difference in interval of the input increased by 1, the difference in outputs of the corresponding inputs increased by 8. A constant increment in the interval between inputs led to a constant increment in the intervals of the corresponding outputs

Answer 2

(a) 8

(b) 16

(c) 24

(d) The ratios are the same

Explanation:

(a) For inputs -5 and -4, the difference of outputs is ...

-3 -(-11) = 8

__

(b) For inputs 0 and 2, the difference of outputs is ...

45 -29 = 16

__

(c) For inputs -3 and 0, the difference of outputs is ...

29 -5 = 24

__

(d) The ratios of output difference over input difference are ...

8/1 = 16/2 = 24/3 = 8 . . . . . they are all the same

This is yet another confirmation that the slope of a line is the same everywhere, and over any interval.