Final answer:
The function h(x) = 57 - 6x + 5x² is nonlinear because it includes the term x².
Step-by-step explanation:
The function h(x) = 57 - 6x + 5x² is nonlinear because it includes the term x².
A linear function is a function that can be represented by a straight line, with a constant rate of change between the input and output values. In this function, the term x² represents a quadratic term, which means the rate of change is not constant, and the graph of the function will not be a straight line.
For example, let's compare the function h(x) = 57 - 6x + 5x² to a linear function, such as f(x) = 2x + 3. If we plot the points for both functions on a graph, we will see that the points for h(x) form a curve, while the points for f(x) form a straight line.