Question

choose the function that is nonlinear. 4x - 8 = 2y; 3y = 6x + 15; y = 2x³ - x² + 5; y = 5x - 19

Explanation:

Step1: Recall linear function definition

A linear function has the form \( y = mx + b \) (or equivalent), where the highest power of the variable is 1. Non - linear functions have a variable with a power other than 1 (e.g., 2, 3, etc.).

Step2: Analyze each option

• For \( 4x - 8=2y \), we can rewrite it as \( y = 2x - 4 \), which is linear (highest power of \( x \) is 1).
• For \( 3y = 6x + 15 \), divide by 3: \( y = 2x+5 \), linear (highest power of \( x \) is 1).
• For \( y = 2x^{3}-x^{2}+5 \), the highest power of \( x \) is 3, so it is non - linear.
• For \( y = 5x - 19 \), linear (highest power of \( x \) is 1).

Answer:

\( y = 2x^{3}-x^{2}+5 \) (the function in the orange box)