What you’ll learn
Sketch graphs from verbal descriptions.
Key idea
Graph construction must preserve both the changing interval and the constant interval, with named horizontal and vertical coordinates.
Preserve the change point and both segment behaviors; isolated points alone do not establish the connecting shape.
Worked example
Enter the exact value or ordered values in the format requested below.
Read the transition x-coordinate of straight graph segments A→B→C, x horizontal and y vertical.
Marked coordinates: B=(3, 0); C=(6, 0); A=(0, -3).
- Straight segment A(0,-3) to B(3,0) rises; segment B to C(6,0) is horizontal.
- Transition input is 3; graph vertices are {(0,-3),(3,0),(6,0)}; integer-input table is [(0, -3), (1, -2), (2, -1), (3, 0), (4, 0), (5, 0), (6, 0)].
Answer: 3
Quick Check
Relate the graph used in 'Sketch graphs from verbal descriptions' to an equation, table, transformation, or verbal description.
Connect straight graph A→B→C to a full integer-input table over 0 through 6.
Marked coordinates: B=(3, 5); C=(6, 5); A=(0, -1).