Question

Determine the type of function each table represents. Write “linear”, “exponential”, or “neither”.

Two-way table with x-values 0, 1, 2, 3, 4 and y-values 0, 1, 4, 9, 16
[ Select ]

Two-way table with x-values 0, 1, 2, 3, 4 and y-values 1/3, 1, 3, 9, 27
[ Select ]

Two-way table with x-values 0, 1, 2, 3, 4 and y-values 5, 5/2, 5/4, 5/8, 5/16
[ Select ]

Two-way table with x-values 0, 1, 2, 3, 4 and y-values 4.5, 4, 3.5, 3, 2.5
[ Select ]

Answer 1

Explanation:

Linear

Answer 2

1) Neither

2) Exponential

3) Exponential

4) Linear

Explanation:

1) x-values
`{}` y-values

0
`{}` 0

1
`{}` 1

2
`{}` 4

3
`{}` 9

4
`{}` 16

Therefore, we have, the relationship of the function given as_f(x) = x² Which is neither a linear function nor an exponential function

2) x-values
`{}` y-values

0
`{}` 1/3

1
`{}` 1

2
`{}` 3

3
`{}` 9

4
`{}` 27

The relationship between 'x', and 'y' is given as follows;

f(x) = 3⁽ˣ⁻¹⁾

Therefore, the relationship between 'x', and 'y', is an exponential relationship, and the function is an exponential function

3) x-values
`{}` y-values

0
`{}` 5

1
`{}` 5/2

2
`{}` 5/4

3
`{}` 5/8

4
`{}` 5/16

The relationship between 'x', and 'y' is given as follows;

f(x) = 5×(1/2)ˣ

Therefore, the relationship between 'x', and 'y', is an exponential relationship, and the function is an exponential function

4) x-values
`{}` y-values

0
`{}` 4.5

1
`{}` 4

2
`{}` 3.5

3
`{}` 3

4
`{}` 2.5

The given data for the y-values has a constant first common difference of 4 - 4.5 = -0.5, therefore, the relationship between the 'x', and 'y' values is a linear relationship.