Question

1. determine if each function is linear or nonlinear.

drag each function into a box to correctly classify it.
linear
nonlinear
$y = \frac{x}{4} - 2$
$y = 3x^2 + 5$
$y = \frac{4}{x} - 3$
$3x + y = 12$
$y = x$

Explanation:

Step1: Define linear function rule

A linear function has the form $y=mx+b$ (or $Ax+By=C$), where the highest power of $x$ is 1, no variable products/powers >1.

Step2: Classify each function

1. $y=\frac{x}{2}-2$: Power of $x$ is 1 → Linear
2. $y=3x^2+5$: Power of $x$ is 2 → Nonlinear
3. $y=\frac{5}{x}-3$: Equals $5x^{-1}-3$, power of $x$ is -1 → Nonlinear
4. $3x+y=12$: Rewrites to $y=-3x+12$, power of $x$ is 1 → Linear
5. $y=x$: Power of $x$ is 1 → Linear

Answer:

Linear:

$y=\frac{x}{2}-2$, $3x+y=12$, $y=x$

Nonlinear:

$y=3x^2+5$, $y=\frac{5}{x}-3$