The problem requires us to determine whether the given functions are linear or nonlinear. The functions are: $y = \frac{1}{2}x + 1$ $y = 3x - 1$ $y = \frac{1}{x} - 2$ $y = 2$

1. Problem Description

The problem requires us to determine whether the given functions are linear or nonlinear. The functions are:

$y = \frac{1}{2}x + 1$

$y = 3x - 1$

$y = \frac{1}{x} - 2$

$y = 2$

2. Solution Steps

A linear function has the general form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Any function that cannot be written in this form is nonlinear.

* Function 1: $y = \frac{1}{2}x + 1$

This function is in the form $y = mx + b$, where $m = \frac{1}{2}$ and $b = 1$. Thus, it is a linear function.

* Function 2: $y = 3x - 1$

This function is in the form $y = mx + b$, where $m = 3$ and $b = -1$. Thus, it is a linear function.

* Function 3: $y = \frac{1}{x} - 2$

This function can be rewritten as $y = x^{-1} - 2$. Since the exponent of $x$ is -1, this function is not linear. It is a nonlinear function.

* Function 4: $y = 2$

This function can be written as $y = 0x + 2$, which is in the form $y = mx + b$, where $m = 0$ and $b = 2$. Thus, it is a linear function.

3. Final Answer

$y = \frac{1}{2}x + 1$: Linear

$y = 3x - 1$: Linear

$y = \frac{1}{x} - 2$: Nonlinear

$y = 2$: Linear