Tensor by Tensor

MODULE 01 · LESSON 01

Functions

A function is one rule that turns each allowed input into one output.

PLAIN-LANGUAGE INTRODUCTION

What is this?

A function is one rule that turns each allowed input into one output.

One simple example

Use f(x) = 2x + 1. For x = 3, the output is 7.

What goes in?

One allowed value. Here, x is 3.

What comes out?

The rule’s result. Here, f(3) is 7.

Why does it matter?

Models are functions with adjustable numbers inside their rules.

What is it not?

A function is not a list of guesses. Its rule fixes each output.

WORK THROUGH THE IDEA

See the idea in more detail

  1. The symbol f names the function. The symbol x names its input.
  2. Send in x = 3. The rule says to multiply by 2, then add 1.
  3. First compute 2 × 3 = 6. Then compute 6 + 1 = 7.
  4. So f(3) = 7. The plotted points show the same rule for four inputs.
  5. Common mistake: f(x) does not mean f × x. It means the output from f.
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