Question

which equations represent nonlinear functions? select all that apply. select all correct options
y=2x^3
y=9x^2+7x
y=3x - 4
2x^2 = y + 4
y = x

Explanation:

Step1: Recall linear function definition

A linear function has the form \( y = mx + b \) (or can be rewritten in this form), where the highest power of \( x \) is 1. A nonlinear function has a highest power of \( x \) greater than 1 (or other non - linear forms like absolute value, square root, etc., but here we deal with polynomials).

Step2: Analyze \( y = 2x^{3}\)

The highest power of \( x \) is 3, which is greater than 1. So this is a nonlinear function.

Step3: Analyze \( y=9x^{2}+7x\)

The highest power of \( x \) is 2, which is greater than 1. So this is a nonlinear function.

Step4: Analyze \( y = 3x - 4\)

This is in the form \( y=mx + b\) with \( m = 3\) and \( b=-4\), and the highest power of \( x \) is 1. So this is a linear function.

Step5: Analyze \( 2x^{2}=y + 4\)

Rewrite it as \( y=2x^{2}-4\). The highest power of \( x \) is 2, which is greater than 1. So this is a nonlinear function.

Step6: Analyze \( y=x\)

This is in the form \( y = mx + b\) with \( m = 1\) and \( b = 0\), and the highest power of \( x \) is 1. So this is a linear function.

Answer:

\( y = 2x^{3}\), \( y=9x^{2}+7x\), \( 2x^{2}=y + 4\)