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Math 110090 (10772) Learning Outcomes and Indicators
Learning Goals
General Function Knowledge
 Understand functional notation

Domain, Range

Construct and interpret graphs
including piecewise

Model: Recognize linear and nonlinear functions from formulas,
graphs, and/or tables; use regression
feature on calculator to find line of
best fit.
Assessment Ideas
2. The table shows the average price of a gallon of milk and the average price of a gallon
of gasoline during the last 6 months of 2014. Which of the statements apply to the data in
the table? Choose the BEST answer
Month 1
2
3
4
6
Milk
$1.79 $2.29 $2.19 $1.89 $2.09 $2.29
Gas
$1.93 $1.96 $1.79 $1.69 $1.98 $1.80
A) Milk is a function of Gas
B) Gas is a function of Milk
C) Gas is a function of Month
D) Both A) and C)
E) Both B) and C)
Linear functions/Systems of linear equations
(2 variables)
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2
Write linear function given:

Two solutions, parameters, or one
parameter one solution

Apply and interpret in application
problems:

Parameters

Find specific solution given one
variable

Graph solution set [also linear
inequalities]
You have just been hired as a product manager for a manufacturing firm. Your first job is
to analyze the data for three products (designated A, B, and C) and make some
recommendations.
Your product analysts have supplied you with the price-supply and price-demand
equations for all three products A, B, and C, as well as the fixed and variable costs for
each product. The data is shown in the table below.
Price-supply
Price-demand
Fixed Cost
Variable Cost
A
p = 1.1q
p = 1008 – 3.1q
50000
20
B
p = 1.3q
p = 1127 – 3.6q
200000
15
C
p = 1.9q
p = 1040.3 – 2.14q
50000
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Assume that you will be selling each product at its equilibrium price. Determine the cost
C(x), revenue R(x), and simplified profit P(x) functions for all three products.
If you assume the number of each product you will sell will equal the equal equilibrium
demand for the product, how much profit or loss will you make on each? Should you go
ahead with production of each product? Why or why not please explain.
Quadratic functions
Given formula:

Find critical points
Apply and interpret in application
problems:

Critical points

Find specific solutions given one
variable

Graph solution set
Additional Topics with functions
The gas mileage, M, for a certain new car is modeled by the function
𝑀(𝑠) = (−1/28) 𝑠 2 + 3𝑠 − 31 where s is the speed in mph and M is measured in
miles per gallon. At what speed is the gas mileage a maximum?
or
Suppose that the manufacturer of a product has found that, when producing and selling x
units of a product, the profit P (in thousands of dollars) is given by
P( x)  3 x 2  36 x
How many should the company make and sell in order to earn $81 thousand dollars
profit?
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Understand function compositions

Understand function inverses and its
usefulness.
Exponential/log functions
Write exponential function given:

Two solutions, parameters, or one
parameter and one solution

Apply and interpret in application
problems:
o Parameters
o Find specific solution given
one variable
o Graph solution set

Change between exponential and
logarithmic forms using properties
of logarithms
You just received a mystery discount coupon for a local department store. When the discount was
revealed you were in luck, it was a 30% discount on all purchases.
A. Define the function, D(x) that represents your dollar amount spent at the store based on the
retail price x of the merchandise purchased.
B. If your retail price for all merchandise purchased today is $105. 00 how much money do
you need to give to the cashier? (Neglect sales tax in this application)
C. Now let’s say you have $20.00 in Krazy Cash for this same store. If you only used this
“purchase perk” define this function as K(x) where K(x) represent the dollar amount you
will give to the cashier and x represents the retail price of the items purchased.
D. Let’s now say that the store will allow you to use both the 30% discount and your $20.00
Krazy Cash for your purchase, the $20. Krazy Cash first followed by the 30%. If you
bought $105.00 dollars today how much money would you give the cashier?
E. Define this composition of the two functions D (K(x)) both symbolically and numerically.
F. Now let’s assume the store will allow you to use the discount first followed by the $20.00
Krazy cash. Form this new composition both symbolically and numerically. Which is
the better deal?
The population of a certain city was 220,000 in the year 2010 and has an annual growth
rate of 1.7%. Using the growth factor, find a function that models the population of this
city t years after the year 2010.
At the end of an advertising campaign, sales amounted to $30,000 and then decreased 4%
each week. Using the decay factor, write the equation of the exponential function that
models the sales t weeks after the campaign.
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Polynomial Functions
Identify graphs of higher degree
polynomials and identify and
interpret critical points of the graph
in context
Model data with higher order
polynomials, determine which type
of function best models the data
Given a graph solve a polynomials
inequality in context.
Use the graph of 𝑓(𝑥)to find the factorization of
𝑓(𝑥) = −𝑥 4 + 5𝑥 3 + 3𝑥 2 − 13𝑥 − 10
A) (𝑥 + 1)(𝑥 − 2)(𝑥 − 5)2
B) −(𝑥 + 1)(𝑥 − 2)(𝑥 2 − 5)
C)
(𝑥 − 1)(𝑥 + 2)(𝑥 2 + 5)
D)
−(𝑥 − 1)(𝑥 + 2)(𝑥 2 + 5)
E) −(𝑥 + 1)(𝑥 − 2)(𝑥 − 5)2