Question

For each function, state whether it is linear, quadratic, or exponential.

Answer 1

Explanation:

Table for function 1,

x y Difference 1 Difference 2

2 10 - -

3 1 1 - 10 = -9 -

4 10 10 - 1 = 9 9 - (-9) = 18

5 37 37 - 10 = 27 27 - 9 = 18

6 82 82 - 37 = 45 45 - 27 = 18

Since, difference 2 is common as 18,

Table will represent a quadratic function.

Table for function 2,

x y Difference 1 Difference 2

5 16 - -

6 19 19 - 16 = 3 -

7 28 28 - 19 = 9 9 - 3 = 6

8 43 43 - 28 = 15 15 - 9 = 6

9 64 64 - 43 = 21 21 - 15 = 6

Since, difference 2 is common as 6,

Table will represent a quadratic function.

Table for function 3,

x y Ratio

1 112 -

2 56 56 ÷ 112 =
`(1)/(2)`

3 28 28 ÷ 56 =
`(1)/(2)`

4 14 14 ÷ 28 =
`(1)/(2)`

5 7 7 ÷ 14 =
`(1)/(2)`

Since, ratio is common as
`(1)/(2)`.

Table will represent an exponential function.