AP®︎ Precalculus: Topic 2.11 Practice Test

Essential Knowledge: 2.11.A.1

The domain of a logarithmic function in general form is any real number greater than zero, and its range is all real numbers.

Essential Knowledge: 2.11.A.2

Because logarithmic functions are inverses of exponential functions, logarithmic functions are also always increasing or always decreasing, and their graphs are either always concave up or always concave down. Consequently, logarithmic functions do not have extrema except on a closed interval, and their graphs do not have points of inflection.

Essential Knowledge: 2.11.A.3

The additive transformation function $g(x)=f(x+k)$, where $k\ne 0$, of a logarithmic function $f$ in general form does not have input values that are proportional over equal-length output-value intervals. However, if the input values of the additive transformation function, $g(x)=f(x+k)$, of any function $f$ are proportional over equal-length output value intervals, then $f$ is logarithmic.

Essential Knowledge: 2.11.A.4

With their limited domain, logarithmic functions in general form are vertically asymptotic to $x=0$, with an end behavior that is unbounded. That is, for a logarithmic function in general form, $\lim_{x\to 0^+}a\log_b x=\pm\infty$ and $\lim_{x\to\infty}a\log_b x=\pm\infty$.