To classify the functions f(x), g(x), and h(x), we need to analyze their forms.
1. f(x) = 4x²: This function is quadratic because it has the form of ax², where a is a constant (in this case, 4). Quadratic functions are characterized by the x raised to the power of 2, which means the graph will be a parabola.
2. g(x) = 1/x: This function is neither linear nor quadratic; instead, it is classified as rational. However, if we consider it with respect to polynomials, it does not fit either the linear or quadratic criteria. It’s a hyperbola and represents a type of function that involves division by x.
3. h(x) = 32x: This function is linear, characterized by the form mx + b where m and b are constants. In this case, 32 is the coefficient (m) of x, and there is no constant term (b). The graph of a linear function is a straight line.
In summary:
- f(x) = 4x² is quadratic.
- g(x) = 1/x is rational.
- h(x) = 32x is linear.