AP®︎ Precalculus: Topic 1.4 Practice Test

Essential Knowledge: 1.4.A.1

A nonconstant polynomial function of $x$ is any function representation that is equivalent to the analytical form $p(x) = a_nx^n + a_{n-1}x^{n-1} + a_{n-2}x^{n-2} + \ldots + a_2x^2 + a_1x + a_0$, where $n$ is a positive integer, $a_i$ is a real number for each $i$ from 0 to $n$, and $a_n$ is nonzero. The polynomial has degree $n$, the leading term is $a_nx^n$, and the leading coefficient is $a_n$. A nonzero constant is also a polynomial function of degree zero.

Essential Knowledge: 1.4.A.2

Where a polynomial function switches between increasing and decreasing, or at the included endpoint of a polynomial with a restricted domain, the polynomial function will have a local, or relative, maximum or minimum output value. If any local maximum is greater than all other function output values, then that local maximum is a global, or absolute, maximum. Similarly, if any local minimum is less than all other function output values, then that local minimum is a global, or absolute, minimum.

Essential Knowledge: 1.4.A.3

Between every two distinct real zeros of a nonconstant polynomial function, there must be at least one input value corresponding to a local maximum or local minimum.

Essential Knowledge: 1.4.A.4

A polynomial function of even degree has either a global maximum or a global minimum. For a quadratic function, the global maximum or global minimum occurs at the vertex.

Essential Knowledge: 1.4.A.5

Points of inflection of a polynomial function occur at input values where the rate of change of the function changes from increasing to decreasing or from decreasing to increasing. This occurs where the graph of a polynomial function changes from concave up to concave down or from concave down to concave up.