AP®︎ Precalculus: Topic 2.10 Practice Test

Essential Knowledge: 2.10.A.1

The general form of a logarithmic function is $f(x) = a\log_b x$, with base $b$, where $b > 0$, $b \ne 1$, and $a \ne 0$.

Essential Knowledge: 2.10.A.2

The way in which input and output values vary together have an inverse relationship in exponential and logarithmic functions. Output values of general-form exponential functions change proportionately as input values increase in equal-length intervals. However, input values of general-form logarithmic functions change proportionately as output values increase in equal-length intervals. Alternately, exponential growth is characterized by output values changing multiplicatively as input values change additively, whereas logarithmic growth is characterized by output values changing additively as input values change multiplicatively.

Essential Knowledge: 2.10.A.3

$f(x) = \log_b x$ and $g(x) = b^x$, where $b > 0$ and $b \ne 1$, are inverse functions. That is, $g(f(x)) = f(g(x)) = x$.

Essential Knowledge: 2.10.A.4

The graph of the logarithmic function $f(x) = \log_b x$, where $b > 0$ and $b \ne 1$, is a reflection of the graph of the exponential function $g(x) = b^x$, where $b > 0$ and $b \ne 1$, over the graph of the identity function $h(x) = x$.

Essential Knowledge: 2.10.A.5

If $(s, t)$ is an ordered pair of the exponential function $g(x) = b^x$, where $b > 0$ and $b \ne 1$, then $(t, s)$ is an ordered pair of the logarithmic function $f(x) = \log_b x$, where $b > 0$ and $b \ne 1$.