# Graphing Piecewise Functions

How to graph the given piecewise functions: examples and their solutions.

## Example 1

Draw *y* = 2*x* + 3 (*x* < 0)

on the coordinate plane.

[*x* < 0] doesn't include [*x* = 0].

So draw an empty point

on the *y*-intercept: 3.

Slope-intercept form

Draw *y* = *x* - 1 (*x* ≥ 0)

on the coordinate plane.

[*x* ≥ 0] does include [*x* = 0].

So draw a full point

on the *y*-intercept: -1.

So this is the graph of the given piecewise function.

## Example 2

Draw *y* = *x*^{2} (*x* < 1)

on the coordinate plane.

[*x* < 1] doesn't include [*x* = 1].

So draw an empty point on the graph

at [*x* = 1].

Quadratic function - Vertex form

Draw *y* = *x* (*x* ≥ 1)

on the coordinate plane.

[*x* ≥ 1] does include [*x* = 1].

So draw a full point on the graph

at [*x* = 1].

But the empty point is already on (1, 1).

So fill in the empty point.

The empty point and the full point

are at the same point: (1, 1).

So erase the filled point at (1, 1).

So this is the graph of the given piecewise function.

## Example 3

See the first case of the given piecewise function.

[*x* ≠ 3] means [*x* - 3 ≠ 0].

So cancel (*x* - 3)

on both of the numerator and the denominator.

Then *y* = *x* + 1.

Simplifying rational expressions

So the given piecewise function

can be written like this.

Draw *y* = *x* + 1 (*x* ≠ 3)

on the coordinate plane.

The line doesn't include the point at [*x* = 3].

So draw an empty point on the line

at *x* = 3.

*y* = -2 (*x* = 3)

means (3, -2).

So draw a full point at (3, -2).

So this is the graph of the given piecewise function.