Warm Up State the domain and range of the following equations: y = |x – 2| y = 2x + 3 y = x2

Unit 8 Day 1 Piecewise Functions

Piecewise Function A piecewise function is a function represented by a combination of equations, each corresponding to a part of the domain.

What do they look like? f(x) = x2 + 1 , x  0 x – 1 , x  0 We will work with piecewise functions in two ways: We will evaluate piecewise functions for specific values of x. We will graph piecewise functions.

Evaluating piecewise functions is just like evaluating functions you are already familiar with. Let’s calculate f(2). f(x) = x2 + 1 , x  0 x – 1 , x  0 You are being asked to find y when x = 2. Since 2 is  0, you will only substitute 2 into the second part of the equation.

f(x) = Example 1: 2x + 1, x  0 2x + 2, x  0 Evaluate the following: ? -3 f(5) = 12 ? f(1) = 4 ? f(0) = ? 2

f(x) = Example 2: 3x - 2, x  -2 -x , -2  x  1 x2 – 7x, x  1 Evaluate the following: f(-2) = ? 2 f(3) = -12 ? f(-4) = -14 ? ? f(1) = -6

 f(x) = Example 3: x2 + 1 , x  0 x – 1 , x  0 Determine the shapes of the graphs. Parabola and Line Determine the boundaries of each graph.       Graph the line where x is greater than or equal to zero. Graph the parabola where x is less than zero. 

  f(x) = Example 4: 3x + 2, x  -2 -x , -2  x  1 x2 – 2, x  1 Determine the shapes of the graphs. Line, Line, Parabola Determine the boundaries of each graph.          

Writing Piecewise Equations Piecewise functions are made up of different pieces, like this one!

Example 5: First part equation: Second part equation:

Piecewise Functions First part interval: Second part interval:

Now, we can describe the function!