This document contains information about various math concepts including: 1) Ms. Adams' rate of travel over different time periods while driving to California shown in a graph. 2) A post office flat rate mailing function graphed based on package weight. 3) The greatest integer and rounding functions, their notation, and whether they are continuous.

1. NC Math 3

2.  Ms. Adams is traveling to California to see
her sisters.
She drives at a constant pace:
100 miles the first two hours
210 miles the next three hours
240 miles the next four hours
Create a graph
showing her
rate for each hour.

3.  The post office offers flat-rate mailing of
packages: $1.50 for a package weighing less
than 4 oz, $2.50 for a package weighing 4 oz
to less than 8 oz, and $3.50 for a package
weighing 8 oz to 12 oz.
 Graph this function.
Image source labeled for reuse with modification: https://upload.wikimedia.org/wikipedia/commons/3/37/Small_USPS_Truck.jpg

4.  The greatest integer function returns the
greatest integer LESS THAN OR EQUAL TO the
input value.
 Greatest integer notation: f(x) = 𝑥
or 𝑓 𝑥 = 𝑥 (or occasionally f(x) = [x]).
 Sometimes called “floor function”
 How can it be graphed on a calculator?
 Is this function continuous?

6.  The rounding function returns the integer
based on the decimal values of the input.
 Any decimal value < .5 returns the whole
number part of the input.
 Any decimal value  .5 rounds up to the next
integer.

7. A t-shirt company sells t-shirts for $8 apiece if
five or fewer are sold, $6 apiece if 5-10 are
purchased, or $5 apiece if more than 10 are
purchased.
Why is this considered to be a DISCRETE
function?
Sketch a graph.

8.  Graph piecewise function f shown below:
𝑓 𝑥 =
−2, −6 ≤ 𝑥 < −2
−4 , −2 ≤ 𝑥 < 2
−6 , 2 ≤ 𝑥 < 4