Warm-Up: Graph the following piecewise functions
1 if 1  x  2
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2 if 2  x  3
f (x)  
3 if 3  x  4
4 if 4  x  5

x if x  0
f (x)  
x if x  0
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Objective: Students will be able to identify and graph step functions.
A step function is a piecewise function whose graph is a series of line segments that are
not connected and look like “steps.”
The greatest integer function is an example of a step function. It is
written as
function.”
f (x)   x .
Often it is referred to as a “floor
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The greatest integer function means the greatest integer LESS than or equal to x.
Find each value –
1)

1.5  
4) 5 
2) 9.8  
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3) 15.1  
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5) 3.6  
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6) 9.1  
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Example 7: Graph y  2x
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Graph f (x)  2x 
&
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In many real life situations, when we graph a step function the opposite is true.
Generally, you get charged more for going over a certain value (rather then less!). This
is called a ceiling function.
Here is an example for a car rental. The car rental company charges you by the quarter
mile. For each quarter mile, or fraction there of, you are charged an additional $0.50.
Let’s look at the graph
If the circle is filed in, that means
If the circle is empty, that means
How much does it cost if your drive ¼ miles? 1 mile? 1.1 miles? 1.6 miles?
Example 8: BLS is hiring a bus company to take the students on a field trip. The cost is
$50 per bus and a maximum of 30 students are allowed on each bus. Create a graph
that represents this situation. How many buses are needed if 58,59,60,61 or 62
students go on the trip?
Example 9: A parking garage in Downtown crossing charges $5 per hour or fraction
thereof. Draw a graph that represents this function. How much will it cost to park for 4
½ hours?
Name:
Graph each function.
1. Best Guy Auto Repair charges $60 per hour for fraction thereof for labor. Draw a
graph that represents this situation. How much would you pay if they worked on your
car for 3 hours and 15 minutes?
2. BoostUp Mobile charges you $10 per 100 minutes used. Draw a graph that
represents this situation if you use 0 to 500 minutes. How much will it cost if you use
389 minutes? If AT&T charges your $49.99 for unlimited minutes, after how many
minutes should you switch from BoostUp Mobile to AT&T?
3. BLS is preparing for the SAT next week. They can put 25 students in each
classroom. Draw a graph that represents this function. How many classrooms will
they need for 127 students?
4. Laura charges $12 per hour, or fraction there of, to babysit. Draw a graph that
represents this function. How much will she charge if she works 4½ hours?
5. The post office charges $0.44 for a letter up to 5 ounces to be delivered. After that
they charge $0.05 for each additional ounce or part thereof. Draw a graph that
represents this function. How much will it cost to mail a letter that is 12.5 ounces?
6. f (x)  3 x 
7. f (x)   x 1
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8. f (x)   x 1
9. f (x)  3x 
10. f (x)   x  2 
11. f (x)  2x 1
12. f (x)  2 x  1