# Piecewise Functions

How to graph piecewise functions: examples and their solutions.

## Example 1

[Blue] *x* < 0:

Draw *y* = 2*x* + 1.

Draw an empty circle at *x* = 0.

Slope-intercept form

[Green] *x* ≥ 0:

Draw *y* = *x* - 1.

Draw a full circle at *x* = 0.

## Example 2

[Blue] *x* < 1:

Draw *y* = *x*^{2}.

Draw an empty circle at *x* = 1.

Quadratic function: vertex form

[Green] *x* ≥ 1:

Draw *y* = *x*.

Draw a full circle at *x* = 1.

Both graphs have the same *y* value at *x* = 1.

(1^{2} = 1)

So it's okay to draw the graphs

without the circles at *x* = 1.

## Example 3

Simplifying rational expressions

[Blue] *x* ≠ 3:

Draw *y* = *x* + 1.

Draw an empty circle at *x* = 3.

Excluded value (extraneous solution)

[Green] *x* = 3:*y* = -2

Draw a full circle at (3, -2).