When graphing these, always identify the boundary points first. These are the x-values where the rules switch. Decide if the point is "open" (using is greater than ) or "closed" (using ≤is less than or equal to ≥is greater than or equal to ) to ensure the relation remains a true function. 2. The Step Function: The Logic of the Jump
f(x) = { 2 if x < 1 { 4 if 1 ≤ x < 2 { 6 if x ≥ 2
For problems 1–4, evaluate the function at the given value.
A piecewise function is still a function. If your graph has two closed circles stacked vertically at a boundary, it fails the vertical line test and is incorrect.
Given [ f(x) = \begincases x+1 & x \leq 2 \ 5 & x > 2 \endcases ] State the domain and range.
Graph the step function:
Q: What is the general form of a step function? A: f(x) = { c1 if x ∈ [a, b) { c2 if x ∈ [b, c) { ... { cn if x ∈ [n, ∞)
A water tank has three levels: empty (0-20 gallons), half-full (21-40 gallons), and full (41-60 gallons). The water level is checked at regular intervals, and the tank is filled or emptied accordingly.
Graphing is the heart of the "3-7 skills practice." A correctly drawn graph reveals the function's behavior instantly.