Click each step to learn more.
Step 1: Analyze the pieces of the function.Example:
f(x)=
-negativex2+9,x<2 
The function is quadratic for all x values less than 2.
32x−10,x≥2 The function is linear for all x values greater than or equal 2.
f(x)=
-negativex2+9,x<2 
The function is quadratic for all x values less than 2.
32x−10,x≥2 The function is linear for all x values greater than or equal 2.
The function f1(x)=-negativex2+9f sub 1 of x is equal to negative x squared plus 9 is graphed below.
However, the quadratic piece is only for the domain of x values less than 2. So, the graph is stopped at x=2.
Note the open dot used to mark the end of the functional piece, since the domain is all x values less than 2, but not equal to 2.
f(x)=
-negativex2+9,x<2 The function is quadratic for all x values less than 2.
32x−10,x≥2 
The function is linear for all x values greater than or equal 2.
The function f2(x)=32x−10f sub 2 of x equals three halves x minus ten is graphed below.
However, the linear piece is only for the domain of x values greater than or equal to 2. So, the function begins at x=2 and extends to infinity.
Note the closed dot used to mark the beginning of the functional piece, since the domain is all x values greater than or equal to 2.
Our example only has two pieces, so the graph is complete. Some piecewise functions can have many pieces.
f(x)=
-negativex2+9,x<2 The function is quadratic for all x values less than 2.
32x−10,x≥2 The function is linear for all x values greater than or equal 2.