Aim #43: What are step functions?Homework: Page 161-162 (2-16 even #s only)Do Now: If f(x) = 2x2 - 3x + 4, then find f(x + 3).

Step FunctionsThe [Greatest Integer Function ] function rounds down to the greatest integer less than or equal to the number. Also known as the Floor Function.

Complete the following table: Greatest Integer Functionf(x) = [ x ]

x f(x)-3-2.5-2-1.5-.50.511.52

1) Graph f(x) = [x + 1] 2) Graph f(x) = 3[x]

3) The following piecewise function is an example of a step-function.

a) Graph this function and state the domain and range.

b) Why is this type of function called a step function?

4) Postage rates on envelopes are a great example of step functions. There is a fixed price for a certain range of weights and then another fixed price for another range of weights, etc. Below is the graph of one such price structure.

a) According to this graph, what would be thepostage rate on a letter weighing 1.5 ounces?

b) What would be the postage rate on a letterweighing exactly 3.0 ounces?

c) Write a piecewise defined function for thepostage rates:

d) Why would it be incorrect to state that the range of this function is 0.50 ≤ y ≤ 1.15 ?

5) The table below lists the total cost for parking for a period of time on a street in Albany, N.Y. The total cost is for any length of time up to and including the hours parked. For example, parking for up to and including 1 hour would cost $1.25; parking for 3.5 hours would cost $5.75.

a) Graph the step function that would represent this situation.

c) Explain how the cost per hour to park changes over the six-hour period.

b) Write it as a piecewise function.

6) A long-distance call to a city in Europe initially costs $4.50 up to the first minute. For one full minute up to two minutes, the cost increases by $0.50; it increases another $0.50 for two full minutes up to three minutes, and so on. The greatest integer step function graphed below illustrates this pricing.

a) What is the cost of a 5 minute and 40 second call?

b) What is the difference between the cost of the call in part a and the cost of an 8 minute call?

c) About how many minutes could you talk for on a phone call that cost $7.50? Give two possible answers.

d) Write the function c(m) to represent the cost for any given time.

Sum It Up!• Piecewise functions can be used to model many real life situations.

• A step function has a constant output and resembles steps when graphed.

HW #43 Answers