Which of the following is a linear function?

• A. y = 3x + 2
• B. y = x^2 + 1
• C. y = sin x.
• D. y = e^x.

Answer: (A)

A linear function is a function whose graph is a straight line, which happens when x appears to the first power and there are no nonlinear operations involved. In y = 3x + 2, x is linear, the slope is constant at 3, and the intercept is 2, so the graph is a straight line. The other expressions are not linear: x^2 adds a squared term and curves into a parabola, sin x is periodic and curved, and e^x grows exponentially, none of which form a straight line.