AP®︎ Precalculus: Topic 1.1 Practice Test

Essential Knowledge: 1.1.A.1

A function is a mathematical relation that maps a set of input values to a set of output values such that each input value is mapped to exactly one output value. The set of input values is called the domain of the function, and the set of output values is called the range of the function. The variable representing input values is called the independent variable, and the variable representing output values is called the dependent variable. Two functions, $f$ and $g$, are equal if they have the same domain, and for every input value $a$ in that same domain, both functions yield the same output value ($f(a)=g(a)$).

Essential Knowledge: 1.1.A.2

The input and output values of a function vary in tandem according to the function rule, which can be expressed graphically, numerically, analytically, or verbally. The image of an input value is the single output value yielded by the function rule. The preimage of an output value is the set of input values for which the function rule yields that output value.

Essential Knowledge: 1.1.A.3

A function is increasing over an interval of its domain if, as the input values increase, the output values always increase. That is, for all $a$ and $b$ in the interval, if $a < b$, then $f(a) < f(b)$.

Essential Knowledge: 1.1.A.4

A function is decreasing over an interval of its domain if, as the input values increase, the output values always decrease. That is, for all $a$ and $b$ in the interval, if $a < b$, then $f(a) > f(b)$. Exclusion: Discriminating between open intervals and closed intervals as it relates to intervals on which a function is increasing or intervals on which a function is decreasing is outside the scope of the AP Precalculus course and exam.

Essential Knowledge: 1.1.B.1

The graph of a function displays a set of input-output pairs and shows how the values of the function’s input and output values vary.

Essential Knowledge: 1.1.B.2

A verbal description of the way aspects of phenomena change together can be the basis for constructing a graph.

Essential Knowledge: 1.1.B.3

The graph of a function is concave up on intervals in which the rate of change is increasing.

Essential Knowledge: 1.1.B.4

The graph of a function is concave down on intervals in which the rate of change is decreasing.

Essential Knowledge: 1.1.B.5

The graph intersects the $x$-axis when the output value is zero. The corresponding input values are said to be zeros of the function.