The classification of the functions as linear or nonlinear is as follows:
Linear Functions:
a) f(x) = 2x - 1
c) g(x) = -0.5x + 3
Nonlinear Functions:
b) h(x) = x^2 + 3
d) k(x) = sin(x)
A linear function is known by its constant rate of change or slope. There is a proportional change in the output following a change in the input.
A nonlinear function does not have a constant rate of change because the change in output is not proportional to the change in the input.
Function b: h(x) = x^2 + 3 is a quadratic function and function d) k(x) = sin(x) is a sinusoidal function, which are nonlinear functions.
Complete Question:
Drag the tiles to the table to classify the functions as linear or nonlinear.
a) f(x) = 2x - 1
b) h(x) = x^2 + 3
c) g(x) = -0.5x + 3
d) k(x) = sin(x)