Question

choose the function that is nonlinear.
14x - 8 = 2y
3y = 6x + 15
(y = 2x^3 - x^2 + 5)
(y = 5x - 19)

Explanation:

Step1: Recall linear function definition

A linear function has the form \( y = mx + b \) (or can be rewritten to this form), where the highest power of \( x \) is 1. Nonlinear functions have \( x \) with a power other than 1 (like \( x^2 \), \( x^3 \), etc.).

Step2: Analyze each option

• Green option (\( 14x - 8 = 2y \)): Rewrite as \( y = 7x - 4 \). Highest power of \( x \) is 1 (linear).
• Purple option (\( 3y = 6x + 15 \)): Rewrite as \( y = 2x + 5 \). Highest power of \( x \) is 1 (linear).
• Orange option (\( y = 2x^3 - x^2 + 5 \)): The term \( x^3 \) (power 3) and \( x^2 \) (power 2) are present. Highest power of \( x \) is 3 (not 1), so it is nonlinear.
• Blue option (\( y = 5x - 19 \)): Highest power of \( x \) is 1 (linear).

Answer:

\( y = 2x^3 - x^2 + 5 \) (the orange - colored function)