Which statement describes a non-linear function?

Which statement describes a non-linear function?

• A. Its graph is not a straight line and does not have a constant rate of change
• B. Its graph is a straight line with constant slope
• C. It passes through the origin only
• D. It is always increasing

Answer: (A)

Non-linear functions have graphs that bend or curve, so the graph is not a straight line and the rate at which the output changes relative to the input isn’t constant. This changing rate of change means the slope isn’t the same everywhere, which is the hallmark of non-linearity. A straight line with constant slope describes a linear function, which is the opposite idea. Statements about passing through the origin or being always increasing don’t define non-linearity—curved graphs can pass through the origin or change from increasing to decreasing or vice versa. So the best description is the one that says the graph isn’t a straight line and the rate of change varies, like how y = x^2 curves and its slope grows larger as x moves away from zero.

Non-linear functions have graphs that bend or curve, so the graph is not a straight line and the rate at which the output changes relative to the input isn’t constant. This changing rate of change means the slope isn’t the same everywhere, which is the hallmark of non-linearity. A straight line with constant slope describes a linear function, which is the opposite idea. Statements about passing through the origin or being always increasing don’t define non-linearity—curved graphs can pass through the origin or change from increasing to decreasing or vice versa. So the best description is the one that says the graph isn’t a straight line and the rate of change varies, like how y = x^2 curves and its slope grows larger as x moves away from zero.