Question

is this function linear or nonlinear?
y = 2x² - 4
nonlinear
linear

Explanation:

Step1: Recall 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: Analyze given function

The function is \( y = 2x^2 - 4 \). Here, the highest power of \( x \) is 2 (from \( x^2 \)), which does not match the linear function form. Functions with a variable raised to a power other than 1 (and no other non - linear operations like square roots, etc. in the simple polynomial case) are nonlinear. So \( y = 2x^2 - 4 \) is a quadratic (nonlinear) function.

Answer:

A. nonlinear