Functions and Their Graphs

A taxi fare depends on the distance. The height of a ball depends on the time. A temperature in kelvin depends on a temperature in celsius. In each case, one number decides another, and mathematics has one word for this: a function. In this chapter we start from sets and relations, and we build the idea of a function with care. Then we draw functions, move and stretch their graphs, combine them, and undo them with the inverse. Python draws the graphs and checks our answers.

Part of Mathematics · High School (11–12) (chapter 1)

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Sets, Relations and Functions

How many students in a class like neither tea nor coffee, when you know how many like each, and how many like both? Sets answer this kind of question. In this course we learn the language of sets, we pair the elements of two sets in relations, and we find the special relation that we call a function, with its domain and its range.

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Graphs and Special Functions

A picture of a function tells you in a moment what a formula hides. In this course we read and draw the graphs of the common functions, we meet the modulus and the greatest integer function, and we learn how to move, stretch and flip a graph. We also learn to see even, odd, increasing and decreasing functions in a picture.

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More onFunctions and Calculus › Graphs of Functions Functions and Calculus › Composite and Inverse Functions Functions and Calculus › Relations and Functions Functions and Calculus › Functional Equations Functions and Calculus › Sets and Intervals Functions and Calculus › Functions as Models of Data Functions and Calculus › Counting Functions