Warm up
1. Find f(6).
4
2. Find g(2).
-2
3. Given r(x) = 2x – 1,
evaluate the domain
{0, 1, 2, 3}. What is
the range of r(x)?
Range: {-1, 1, 3, 5}
Review HW
Skills Check
•Pencil & calculator only
•When finished, flip it over, and
sit quietly.
UNIT QUESTION: How can we use real-world
situations to construct and compare linear and
exponential models and solve problems?
Standards: MCC9-12.A.REI.10, 11, F.IF.1-7, 9,
F.BF.1-3, F.LE.1-3, 5
Essential Question: What is an exponential
function and how is different from a linear
function? What does their point of intersection
represent?
Exponential Functions
An exponential function is a function
of the form y  a  b ,
x
where a  0, b  0, and b  1,
and the exponent must be a variable.
First, let’s take a look at an
exponential function
y2
x
x
y
-2
1/4
-1
1/2
0
1
1
2
2
4
y  a b
x
So our general form is simple enough.
The general shape of our graph will be determined by the
exponential variable.
Which leads us to ask what role does the ‘a’ and
the base ‘b’ play here. Let’s take a look.
First let’s change the base b
to positive values
What conclusion can
we draw ?
y  a b
x
To see what impact ‘a’ has on our graph
we will fix the value of ‘b’ at 3. We are going to look at
positive values of a today.
What does a larger
value of ‘a’
accomplish ?
Linear, Exponential, or
Neither
For each representation of a function, decide
if the function is linear, exponential, or
neither. Give reasons for your answer.
1.
Linear
For each representation of a function, decide
if the function is linear, exponential, or
neither. Give reasons for your answer.
2.
Exponential
Rounds of Tennis
1
2
3
4
5
Number of Players
left in Tournament
64
32
16
8
4
For each representation of a function, decide
if the function is linear, exponential, or
neither. Give reasons for your answer.
3. This function is decreasing at a constant rate.
Linear
For each representation of a function, decide
if the function is linear, exponential, or
neither. Give reasons for your answer.
4. A person’s height as a function of a person’s
age (from age 0 to100).
Neither
For each representation of a function, decide
if the function is linear, exponential, or
neither. Give reasons for your answer.
5.
Linear
For each representation of a function, decide
if the function is linear, exponential, or
neither. Give reasons for your answer.
6. Each term in a sequence is exactly 1/3 of
the previous term.
Exponential
INTERSECTIONS OF
GRAPHS
Points of Intersection
LINEAR VS. EXPONENTIAL
FUNCTIONS TASK
Classwork
Option 1: You can have $1000 a year for twenty years.
Option 2: You can get $1 the first year, $2 the second
year, $4 the 3rd, doubling the amount each year for
twenty years.
Which option
gives you
more
money?
RAKING LEAVES TASK
Classwork
1. Two dollars for each bag of leaves.
2. Or two cents for one bag, four cents for two bags,
eight cents for three bags, and so on with the amount
doubling for each additional bag.
1. If Celia rakes
five bags of
leaves, should
she opt for
payment method
1 or 2? What if
she rakes ten
bags of leaves?
1. Two dollars for each bag of leaves.
2. Or two cents for one bag, four cents for two bags,
eight cents for three bags, and so on with the amount
doubling for each additional bag.
2. How many
bags of leaves
does Celia have
to rake before
method 2 pays
more than
method 1?
1. Two dollars for each bag of leaves.
2. Or two cents for one bag, four cents for two bags,
eight cents for three bags, and so on with the amount
doubling for each additional bag.
3. Describe the
differences in
payment
plans.
1. Two dollars for each bag of leaves.
2. Or two cents for one bag, four cents for two bags,
eight cents for three bags, and so on with the amount
doubling for each additional bag.
4. Describe the
difference in the
way the payment
grows in the
table and on the
graph.
1. Two dollars for each bag of leaves.
2. Or two cents for one bag, four cents for two bags,
eight cents for three bags, and so on with the amount
doubling for each additional bag.
5. Is this growth
situation
continuous or
discrete?
How do you
know?
TALK IS CHEAP TASK
Homework