AP®︎ Precalculus: Topic 2.2 Practice Test

Essential Knowledge: 2.2.A.1

Linear functions of the form $f(x) = b + mx$ are similar to arithmetic sequences of the form $a_n = a_0 + dn$, as both can be expressed as an initial value ($b$ or $a_0$) plus repeated addition of a constant rate of change, the slope ($m$ or $d$).

Essential Knowledge: 2.2.A.2

Similar to arithmetic sequences of the form $a_n = a_k + d(n - k)$, which are based on a known difference, $d$, and a $k$th term, linear functions can be expressed in the form $f(x) = y_i + m(x - x_i)$ based on a known slope, $m$, and a point, $(x_i, y_i)$.

Essential Knowledge: 2.2.A.3

Exponential functions of the form $f(x) = ab^x$ are similar to geometric sequences of the form $g_n = g_0r^n$, as both can be expressed as an initial value ($a$ or $g_0$) times repeated multiplication by a constant ratio ($b$ or $r$).

Essential Knowledge: 2.2.A.4

Similar to geometric sequences of the form $g_n = g_kr^{(n-k)}$, which are based on a known ratio, $r$, and a $k$th term, exponential functions can be expressed in the form $f(x) = y_i b^{(x-x_i)}$ based on a known ratio, $b$, and a point, $(x_i, y_i)$.

Essential Knowledge: 2.2.A.5

Sequences and their corresponding functions may have different domains.

Essential Knowledge: 2.2.B.1

Over equal-length input-value intervals, if the output values of a function change at constant rate, then the function is linear; if the output values of a function change proportionally, then the function is exponential. For an exponential function, the known ratio cannot be 0 or 1.

Essential Knowledge: 2.2.B.2

Linear functions of the form $f(x) = b + mx$ and exponential functions of the form $f(x) = ab^x$ can both be expressed analytically in terms of an initial value and a constant involved with change. However, linear functions are based on addition, while exponential functions are based on multiplication.

Essential Knowledge: 2.2.B.3

Arithmetic sequences, linear functions, geometric sequences, and exponential functions all have the property that they can be determined by two distinct sequence or function values.