Functions and their notation

What makes a relation a function, the vertical line test, function notation f(x), evaluating functions, and domain and range.

Functions

A function gives exactly one output for each input. On a graph, every vertical line crosses it at most once (the vertical line test). We write $f(x) = 3x - 2$, so $f(4) = 3(4) - 2 = 10$.

Example 1●●

If $f(x) = x^2 + 1$, find $f(-3)$ and $f(a + 1)$.

$f(-3) = 9 + 1 = 10$

$f(a + 1) = (a + 1)^2 + 1 = a^2 + 2a + 2$

Flashcards

Vertical line test

Function if every vertical line hits at most once.

Range of $y = x^2$

$y \ge 0$

Domain of $y = sqrt{x}$

$x \ge 0$

Practice

$f(x) = 3x - 2$. Find $f(4)$.
$f(x) = x^2 + 1$. Find $f(-3)$.
$f(x) = x^2 + 1$. Find $f(a + 1)$.
Is a circle a function?
Range of $y = x^2 + 3$?
Domain of $y = \sqrt{x - 2}$?
$g(x) = 2x + 5$. Solve $g(x) = 11$.
$h(x) = x^2 - 4x$. Find $h(4)$.