Honors Analysis
 Mr.
Manker is traveling to California.
He 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 his
distance and time
 What
is the domain of the function? The
range?
 Write the equation of the function for
distance (after time t hours) using piecewise
notation
 What is Mr. Manker’s rate of change (speed)
on the interval (0, 2)?
 What is his speed on the interval (2, 5)?
 What is his speed on the interval (5, 9)?
 What aspects of this scenario aren’t realistic?
Why?
 Write
the domain and range using interval
notation:
 Give
the domain and range using interval
notation:
 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. Is it continuous?
Explain.
 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?

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.
 Graph
piecewise function f shown below:
2𝑥 − 2 − 6 ≤ 𝑥 < −2
𝑓 𝑥 =
𝑥−4 −2≤𝑥 <2
𝑥2 − 6
2≤𝑥<4
2𝑥 + 5 𝑖𝑓 𝑥 < 1
𝑓 𝑥 =
3𝑥 + 2 𝑖𝑓 𝑥 ≥ 1
Solve for k so that function f is continuous:
2𝑥 + 6 𝑖𝑓 𝑥 ≤ 2
𝑓 𝑥 =
𝑘𝑥 + 4 𝑖𝑓 𝑥 > 2
 Solve
for k so that f is continuous:
−2𝑥 + 4 𝑖𝑓 𝑥 < 3
f(x)=
𝑥+𝑘
𝑖𝑓 𝑥 ≥ 3
Jose left the airport and traveled toward the
mountains. Kayla left 2.1 hours later traveling
35 mi/hr faster in an effort to catch up to him.
After 1.2 hours Kayla finally caught up. Find
Jose’s average speed.
 Two
cars 276 miles apart start to travel
toward each other. They travel at rates
differing by 5 mi/hr. If they meet after 6
hours, find the rate of each.
A boat traveled 336 miles downstream and
back. The trip downstream took 12 hours.
The trip back took 14 hours. What is the speed
of the boat in still water? What is the speed of
the current?