Graphing Absolute Value Functions: Split, Graph, Glue

Bars in a function? You can't graph them directly, so get rid of them: split at the switch points, graph each piece, glue. Two worked examples, step by step, with the layout to copy into your notes. In this lecture: • The idea: |x − 2| = x − 2 when x is greater than or equal to 2, and 2 − x when x is less than 2. The switch point is where the inside equals zero • Example 1: y = (x + 3)|x − 2| → x is at least 2: y = x² + x − 6 · x is less than 2: y = −x² − x + 6 (vertex (−1/2, 25/4)) → a sharp corner at (2, 0) where the graph bounces, a smooth crossing at −3; checks (3, 6) and (0, 6) • Example 2: y = |x − 2| + |x + 3| → x is less than −3: y = −2x − 1 · x is between −3 and 2: y = 5 · x at least 2: y = 2x + 1 → a "bathtub" with a flat floor at 5, and why: the two distances always add up to the gap, 5 • The method in three steps: switch points → split and drop the bars → graph each piece in its own region and glue Try this one: y = |x + 1| − |x − 3|. Find the switch points and sketch it. (Answer below, after the spoiler gap) . . . . . Answer: switch points −1 and 3. y = −4 for x is less than −1, y = 2x − 2 for x is between -1 and 3 , y = 4 for x is at least 3: a flat step, a ramp, and another flat step. Ontario: Grade 11–12 functions (absolute value and piecewise functions) TIMELINE 0:00 Intro 0:06 Bars Make Corners 1:28 Example 1: Split It 2:58 Example 1: Graph and Glue 4:46 Example 2: Three Pieces 6:09 Example 2: Graph and Glue 7:27 Recap and Your Turn ━━━━━━━━━━━━━━━━━━━━ Dr. Song Square: math academy in Toronto, Ontario Website: www. drsongsquare.com Contact / enquiries: contactus@drsongsquare.com Music: Bensound.com/free-music-for-videos License code: 4ICWECXMHG5QYOSI Artist: : Benjamin Tissot #math #absolutevalue #functions