Graphing Piecewise-Defined Functions (3.12.2) Flashcards
• Piecewise functions are those that are defined differently on different intervals of the x-axis.
• Piecewise functions are those that are defined differently on different intervals of the x-axis.
Piecewise functions can have different shapes from each other in their various parts. Each part must be graphed separately as you use x-values all along the x-axis.
In this case you will use 2x +1 every time you are considering an x that is equal to or larger than 0.
You will use x every time you are considering an x that is
less than 0. The result in this case is two unrelated lines: one that includes 0 and moves to the right, and one that starts at but does not include 0, and moves to the left. Notice how the endpoints are represented to show whether 0 is included or excluded on each line. This example graphs y equals 4 for every x greater than +3.
Notice the horizontal line that starts at +3 and moves to the right. The function also includes a graph for x +1 for every x that includes and is less than +3. That graphs a downsloping line that includes +3 and moves to the left.
Both lines represent the function. This function uses three different expressions to express itself. The result is three lines each being graphed over its segment of the x-axis. Notice how the endpoints are represented. Notice that the middle line is a line segment with two definite endpoints. The two outer lines each have one definite endpoint but go on infinitely on their segment of the plane.
Piecewise functions can have different shapes from each other in their various parts. Each part must be graphed separately as you use x-values all along the x-axis.
In this case you will use 2x +1 every time you are considering an x that is equal to or larger than 0.
You will use x every time you are considering an x that is
less than 0. The result in this case is two unrelated lines: one that includes 0 and moves to the right, and one that starts at but does not include 0, and moves to the left. Notice how the endpoints are represented to show whether 0 is included or excluded on each line. This example graphs y equals 4 for every x greater than +3.
Notice the horizontal line that starts at +3 and moves to the right. The function also includes a graph for x +1 for every x that includes and is less than +3. That graphs a downsloping line that includes +3 and moves to the left.
Both lines represent the function. This function uses three different expressions to express itself. The result is three lines each being graphed over its segment of the x-axis. Notice how the endpoints are represented. Notice that the middle line is a line segment with two definite endpoints. The two outer lines each have one definite endpoint but go on infinitely on their segment of the plane.
