Absolute value function uses variable in absolute value bars. Most common form is f(x) = |x| with a = 1 and h = k = 0. Range is always non-negative, written as x for x ≥ 0
Constant functions are linear with slope 0 and y-intercept (0,c). Identity function is linear with slope 1 and y-intercept (0,0). Squaring function forms parabolas with positive results for nonzero x. Cubing function raises all values to third power
Domain includes all real numbers without division by zero or negative roots. Domain can be written using interval notation with brackets or parentheses. Domain and range are written from smaller to larger values
Piecewise functions partition their domain into intervals for different definitions. Functions are defined using array of functions and associated subdomains. Subdomains must cover entire domain and be pairwise disjoint. Subdomains can be intervals, points, or unbounded intervals
A function relates inputs to outputs, like a machine with input and output parts. Functions are typically written as "f(x) = ...". Functions can have names like "f" or "g"
Piecewise function behaves differently for different input intervals. Defined by individual expressions for each interval. Written as f(x) = {f1(x), f2(x), f3(x)} for different x values