Unit 1 of 8

Reading Quantities and Graphs

  • 7 lessons
  • Parts 1 to 14

Calculus reads formulas, intervals and graphs constantly, usually without stopping to explain them. This unit makes that reading automatic, starting with substituting values into a formula and keeping track of units, then describing sets of allowed values on the number line.

It then treats a function as a rule that gives one output for each input, reads and plots graphs, draws lines from a slope and an intercept, and measures average rates of change. Absolute value closes the unit, as a distance on the number line and as a graph with a corner.

Every lesson is a pair of videos. The theory part explains the idea and the practice part works through problems. Each lesson page has the definitions and an example for every key term.

Formulas and Number Lines

  1. Reading Formulas and Substituting Values

    How to read a formula as a calculation with a purpose, substitute an input at every place it appears, follow the order of operations, and report the result with its units.

    Theory part 1Practice part 2

  2. Number Lines, Intervals, and Allowed Values

    How to move between words, inequalities, interval notation and a number line, keep track of whether each endpoint is included, and describe the inputs a formula allows.

    Theory part 3Practice part 4

Functions and Graphs

  1. Functions as Input-Output Relationships

    What makes a rule a function, how a domain, a formula and a table describe the same assignment, why different inputs may share an output, and why f(x) never means multiplication.

    Theory part 5Practice part 6

  2. Reading Graphs and Plotting Points

    How to place and read points on coordinate axes, move between a formula, a table and a graph with units in view, choose a scale, and avoid reading more from data than it contains.

    Theory part 7Practice part 8

Lines, Rates, and Distance

  1. Drawing Lines from Slope and Intercepts

    Why a constant ratio of rise to run makes a straight line, how to compute slope from two points, and how to draw a line from its rule or from two of its points.

    Theory part 9Practice part 10

  2. Changing Quantities and Average Rate

    How to measure the change in a quantity, compute its average rate of change over an interval with the right units, and read that rate as the slope of a secant line.

    Theory part 11Practice part 12

  3. Absolute Value as Distance and a Graph

    How absolute value measures distance on the number line, why it is never negative, how to solve a simple distance equation, and how the V-shaped graph comes from those distances.

    Theory part 13Practice part 14