Final answer:
In the options provided, a quadratic function, an exponential function, and an absolute value function all represent nonlinear functions because their graphs are not straight lines but have shapes such as curves and angles.
Step-by-step explanation:
The student has asked which of the following represents a nonlinear function: a. quadratic function b. exponential function c. linear function d. absolute value function.
A nonlinear function is one whose graph does not form a straight line. This would include functions with curves, angles, or shapes other than straight lines. Looking at the given options:
- A quadratic function (a), like y = x², forms a parabola and is therefore nonlinear.
- An exponential function (b), such as y = 2¹, increases at an increasing rate and is also nonlinear.
- A linear function (c), y = mx + b, does form a straight line, so it is not nonlinear.
- An absolute value function (d), like y = |x|, creates a V-shaped graph and is also nonlinear.
Therefore, the options that represent a nonlinear function are: a. quadratic function, b. exponential function, and d. absolute value function.