Question

choose all of the functions that are not linear. $\square\\ y = 5(2x - 1)\quad\square\\ y = x(3 - x)\quad\square\\ y = -2x + 4\quad\square\\ y = \frac{1}{3x} - 5\quad\square\\ y = 5$

Explanation:

Step1: Define linear function form

A linear function has the form $y=mx+b$, where $m$ and $b$ are constants, and the highest power of $x$ is 1.

Step2: Simplify and check $y=5(2x-1)$

Expand: $y=10x-5$. This fits $y=mx+b$, so it is linear.

Step3: Simplify and check $y=x(3-x)$

Expand: $y=3x-x^2$. The power of $x$ is 2, so it is not linear.

Step4: Check $y=-2x+4$

This directly fits $y=mx+b$, so it is linear.

Step5: Check $y=\frac{1}{3x}-5$

Rewrite as $y=\frac{1}{3}x^{-1}-5$. The power of $x$ is -1, so it is not linear.

Step6: Check $y=5$

Rewrite as $y=0x+5$. This fits $y=mx+b$, so it is linear.

Answer:

$y = x(3 - x)$, $y = \frac{1}{3x} - 5$