Question

Which equation represents a nonlinear function?
Responses
A
y = x + 25
8
y = x + 25 8
B y = x³ + 0.75y = x ³ + 0.75
C
y = 3 x + 25
5
y = 3 x + 25 5
D y = -.5x +5

Answer 1

A nonlinear function is one that does not form a straight line when graphed. In mathematical terms, this often includes functions that have exponents other than 1, involve products of variables, or involve other nonlinear operations.

Let's analyze the options provided:

A) \( y = x + 25 \) - This is a linear function (straight line).

B) \( y = x^3 + 0.75 \) - This is a nonlinear function because of the \( x^3 \) term.

C) \( y = 3x + 25 \) - This is a linear function (straight line).

D) \( y = -0.5x + 5 \) - This is also a linear function (straight line).

The only equation that represents a nonlinear function is:

**B)** \( y = x^3 + 0.75 \)