1 Pre-­‐Calculus Name: __________________________________ Homework – Greatest Integer Functions Date: ____________________________________ Determine each value. 1. [-­‐3.99] = 2. [0.9] = 3. –[-­‐π ] = Sketch each BY HAND. You may check with your calculator. Use an x-­‐y chart to graph. f (x) = 2 − [−x]
4. f (x)
= [ x ] + 2 5. x y x y Graph each with your calculator. Use the results from your calculator to help you to sketch the graph. x
6. f (x)
7. f (x) = 1 − ⎡ − ⎤
= 2x − x ⎢⎣ 2 ⎥⎦
Applications. You MAY use your calculator for these problems. 8. A long distance phone service charges $0.40 for the first 10 minutes and $0.05 for each additional minute or fraction thereof. Use the greatest integer function to write the cost C of a call in terms of time t (in minutes). Sketch the graph of this function. ⎛ ⎡t + 2 ⎤ ⎞
9. The number of units in inventory in a small company is given by: N(t)
=
25
⎜⎝ 2 ⎢ 2 ⎥ − t ⎟⎠
where t is the time in months. Sketch the graph of this function. ⎣
⎦
How often must this company replenish its inventory? [ ]