Question

Plsssssssss Help!!!!!

Click to show whether each equation represents a linear or nonlinear function.

Answer 1

`y = x^2 + 1` -- Nonlinear

`y = x^1 + 2` -- Linear

`y = x` --- Linear

`y = 5(x + 2)` --- Linear

`y = x(x)` --- Nonlinear

Explanation:

Required

Categorize each function as linear or nonlinear

First, it should be noted that a linear function has the form
`y = mx + b`.

So, the following question will be solved based on the above form

(a):

`y = x^2 + 1`

This can not be expressed as
`y = mx + b`

Hence, it is a nonlinear function

(b):

`y = x^1 + 2`

This can be further expressed as:

`y = x + 2`

This has the same form as
`y = mx + b`.

Hence, it is a linear function.

(c):

`y = x`

This can be further expressed as:

`y = x + 0`

This has the same form as
`y = mx + b`.

Hence, it is a linear function.

(d):

`y = 5(x + 2)`

This can be further expressed as:

`y = 5x + 10` -- by opening the bracket

This has the same form as
`y = mx + b`.

Hence, it is a linear function.

(e):

`y = x(x)`

This can be further expressed as:

`y = x^2` --- by opening the bracket

This can not be expressed as
`y = mx + b`

Hence, it is a nonlinear function