Math 1 · Unit 2
Introduction to Functions and Graph Behaviors
Six lessons: what a function is, from points to a line, domain and range, reading a graph, graphing stories, and average rate of change. Each card below opens a lesson. Every lesson has practice with hints, a study guide, a worksheet with an answer key, and a lesson plan.
What a Function Is: One In, One Out
A function is a rule where one input gives exactly one output, like a spreadsheet formula. Read f(x) as f of x, see why y is the same thing, then fill in tables and plot the points on the coordinate plane.
Start Unit 2, Lesson 1Connect the Dots: From Points to a Line
Fill in the gaps between the dots: an in-between input like 0.5 has one output too, so it is a point on the same line. The line is all of the points at once. Then sort situations into continuous (connect the dots) and discrete (leave them separate).
Start Unit 2, Lesson 2Domain and Range: The Inputs and the Outputs
Domain is the inputs, the x values. Range is the outputs, the y values. Find a reasonable domain and range in a story, then read both off a graph: how far left and right for the domain, how far down and up for the range. Written in words or as an inequality.
Start Unit 2, Lesson 3Reading a Graph: The Behaviors
The heart of the unit: one checklist for reading any graph. Intercepts, where it climbs and falls, where it is above and below the axis, the highest and lowest points, and what happens at the far ends. Practiced on curves and story graphs that no formula could solve.
Start Unit 2, Lesson 4Graphing Stories: Match the Picture to the Story
Read a graph and tell its story with the behavior words. Sketch a graph from a story by shape: climb, level off, drop, or jump. Then match graphs to stories, including the classic distance-versus-speed mix-up.
Start Unit 2, Lesson 5Average Rate of Change: How Fast It Is Changing
Pick two points. Divide the change in the output by the change in the input: how much it went up or down for each step to the right. From a table, from a graph, and from a rule, then read it back into the story. Positive means climbing, negative means falling. Unit 3 gives this number its real name.
Start Unit 2, Lesson 6Printables for Unit 2
Study guides, worksheets with answer keys, and lesson plans for every lesson in this unit.