Extend function graphing to absolute value, piecewise, and step functions.
Common CoreF-IF.C.7bF-BF.B.3
6 lessons21 short videos5 key concepts, out loud
8.1
Graphing Absolute Value Functions
The V-shaped graph and its vertex
F-IF.C.7b
Key idea
Absolute value functions of the form f(x) = a|x - h| + k produce a symmetric, V-shaped graph with a single turning point called the vertex at (h, k), which serves as the anchor point for graphing.
Learn how to graph V-shaped absolute value functions by finding their vertex and plotting symmetric points on both sides.
Key concept · Lesson 8.1
Find the vertex, then step out
Listen0:00 / 0:20
Transcript. An absolute value graph is a sharp V, not a curve. Its turning point, the vertex, sits at h and k, and h always takes the opposite sign to what you see inside the bars. Plot the vertex first, then step out symmetrically in both directions.
8.2
Transformations of Absolute Value Functions
Shift, stretch, and flip the V
F-BF.B.3
Key idea
To transform the parent function f(x) = |x| into g(x) = a|x - h| + k, use h to shift the vertex horizontally, k to shift it vertically, and a to stretch, compress, or reflect the V-shape.
Learn how to shift, stretch, and flip the V-shaped absolute value graph by changing the numbers in its equation.
Key concept · Lesson 8.2
Move it, stretch it, flip it
Listen0:00 / 0:19
Transcript. Every absolute value graph starts from the same V. The number subtracted inside the bars slides it sideways, and the number added outside lifts it. The factor in front stretches or squashes the arms, and if that factor is negative the whole V opens downward.
8.3
Evaluating Piecewise Functions
Pick the right rule for each input
F-IF.C.7b
Key idea
To evaluate a piecewise function, identify which domain interval contains the input value, then substitute that input only into the corresponding rule.
Learn how to read piecewise function rules, match an input value to its correct interval, and calculate the final output.
Key concept · Lesson 8.3
Choose the rule, then plug in
Listen0:00 / 0:21
Transcript. A piecewise function keeps several rules in one place, each owning a stretch of inputs. Find the interval your input belongs to first, then substitute into that rule only. At a boundary, read the sign carefully: only the rule that includes equality owns that point.
8.4
Graphing Piecewise Functions
Draw a function defined in parts
F-IF.C.7b
Key idea
To graph a piecewise function, graph each algebraic rule only over its specified domain interval, using open circles for strict inequalities and closed circles for inclusive inequalities at the boundary points.
Learn how to construct a piecewise graph by drawing each algebraic rule only within its designated domain interval.
Key concept · Lesson 8.4
One included point per x
Listen0:00 / 0:20
Transcript. Graph each rule only across the interval it owns, then stop. At every boundary, a strict inequality gets an open circle and an inclusive one gets a filled circle. Only one of the two pieces may be filled at a shared boundary, or the graph would fail the vertical line test.
8.5
Step Functions & Real-World Models
Functions that jump from one value to the next
F-IF.C.7b
Key idea
A step function consists of constant horizontal line segments that jump from one value to the next, representing real-world situations where outputs change abruptly at specific thresholds, such as postage rates or parking fees.
Learn how to graph step functions and use them to model real-world scenarios like cellular data plans, shipping costs, and hourly parking rates.
Key concept · Lesson 8.5
Read a step graph
Listen0:00 / 0:20
Transcript. A step function holds one value across a whole interval, then jumps to the next. Draw the flat pieces only, never the vertical risers between them. Each step keeps one filled end and one open end, so no input ever lands on two values at once.
8.6
Review & Assessment
Absolute value and piecewise graphs
Review, practice, quiz and test
Key idea
Review absolute value and piecewise graphs with targeted practice, a practice test, and a chapter test.
This is one chapter of the climb.
Algebra 1 spans 16 chapters, every lesson taught on video with a key concept you can hear, and Vector on hand to answer questions out loud.
