Answer:
[tex]y = x^2 + 1[/tex] -- Nonlinear
[tex]y = x^1 + 2[/tex] -- Linear
[tex]y = x[/tex] --- Linear
[tex]y = 5(x + 2)[/tex] --- Linear
[tex]y = x(x)[/tex] --- Nonlinear
Step-by-step explanation:
Required
Categorize each function as linear or nonlinear
First, it should be noted that a linear function has the form [tex]y = mx + b[/tex].
So, the following question will be solved based on the above form
(a):
[tex]y = x^2 + 1[/tex]
This can not be expressed as [tex]y = mx + b[/tex]
Hence, it is a nonlinear function
(b):
[tex]y = x^1 + 2[/tex]
This can be further expressed as:
[tex]y = x + 2[/tex]
This has the same form as [tex]y = mx + b[/tex].
Hence, it is a linear function.
(c):
[tex]y = x[/tex]
This can be further expressed as:
[tex]y = x + 0[/tex]
This has the same form as [tex]y = mx + b[/tex].
Hence, it is a linear function.
(d):
[tex]y = 5(x + 2)[/tex]
This can be further expressed as:
[tex]y = 5x + 10[/tex] -- by opening the bracket
This has the same form as [tex]y = mx + b[/tex].
Hence, it is a linear function.
(e):
[tex]y = x(x)[/tex]
This can be further expressed as:
[tex]y = x^2[/tex] --- by opening the bracket
This can not be expressed as [tex]y = mx + b[/tex]
Hence, it is a nonlinear function
