Chapter 1 Test Overview: Make sure that you use your quizzes, accuracy checks, homework, and class
notes to study for the test. What we did in class and focused on for homework will be the best indicator of
what you should practice. This should be a supplemental resource.
Section 1.1: Functions
1. Which equations represent y as a function of x?
a.) y  x  2
b.) 𝑥 2 + 𝑦 2 = 4
c.) |𝑥 − 2| = 𝑦
3√−4𝑥
𝑖𝑓 𝑥 ≤ −5
5
𝑖𝑓 − 5 < 𝑥 < 3
|−𝑥 + 2|
𝑖𝑓 𝑥 ≥ 3
2. Evaluate the piecewise function at the given values: 𝑓(𝑥) = {
a.) -3
b.) -10
c.) 3
3. Find the domain for the functions below:
a.) 𝑓(𝑥) = √16 − 𝑥 2
e.) f ( x) 
3
√𝑥+2
b.) 𝑓(𝑥) = 12𝑥+2
c) 𝑓(𝑥) =
6
d.) f ( x)  x 2  8 x
√−𝑥+8
x4
2 x  10
Section 1.2: Analyzing Graphs
y
2
1. Find the intercepts of the function: 𝑓(𝑥) = − 3 𝑥 − 8
2. Use the graphs to determine the domain and range.
a.)

b.)
x



3. If a graph has the point (-2, 5) on it, what other points would be on the graph with the properties below?
a.) The function is even
b.) The function is odd
c.) The graph has x-axis symmetry
4. Algebraically determine if the function is even, odd, or neither:
a.) 𝑓(𝑥) = 2(𝑥 − 1)2 − 3𝑥
𝑥4
d.) 𝑓(𝑥) = 𝑥 2 −2
𝑥
b.) 𝑓(𝑥) = 𝑥 2 −4
c.) 𝑓(𝑥) = (𝑥 2 + 2)(𝑥 3 + 𝑥)
Section 1.3: Continuity, End Behavior, and Limits
1. Use limit notation to describe the left and right end behavior:
a.)
b.)
for c and d use limit notation to describe the rend behavior as x goes to infinity:
c.) 𝑓(𝑥) =
−4𝑥 2 +2
d.) 𝑓(𝑥) = 3𝑥 3 − 2𝑥
𝑥+3
2. Determine if the function is continuous at the given value using the continuity test. If the function is not
continuous, state the type of discontinuity.
𝑥 2 −3𝑥
a.) 𝑓(𝑥) = 𝑥 2 −𝑥−6 at x = 3
c.) 𝑓(𝑥) = {
−𝑥 + 4
4𝑥 + 9
b.)
𝑖𝑓 𝑥 < −1
at x = -1
𝑖𝑓 𝑥 ≥ −1
 4 x  3 if x  6

f  x   2 x  5
if  6  x  3

9
if x  3

d.) 𝑓(𝑥) =
2𝑥+1
𝑥−3
at x = - 6
at x = 3
Section 1.4: Extrema and Average Rates of Change
1. Determine the intervals for which the function is increasing, decreasing, or constant.
y
y
a.)
b.)


x


x




2. Using your graphing calculator find and classify extrema as relative maxima, relative minima, absolute
maxima and absolute minima.
a.) 𝑓(𝑥) = 𝑥 6 − 4𝑥 4 + 𝑥
b.) 𝑓(𝑥) = −0.008𝑥 5 − 0.05𝑥 4 − 0.2𝑥 3 + 1.2𝑥 2 − 0.7𝑥
3. Mr. Plum has 100 bushels of soybeans to sell. The current price of soybeans is $6 a bushel. He expects
the market price of a bushel to rise in the coming weeks at a rate of $0.10 per week. For each week he
waits to sell, he loses 1 bushel due to spoilage.
a.) Write a function to model P in terms of w (profit in terms of number of weeks). Graph the function and
determine the domain.
b.) When should Mr. Plum sell the soybeans in order to maximize his income? What will the income be?
4. The owner of a farm has 30 regular workers who each bring the farm a profit of $200 per day. For each
additional worker hired, the total profit per worker decreases by $2.75 per day. How many additional
workers should the owner hire to maximize profits?
5. A baseball team plays in a stadium that holds 60,000 spectators. With the ticket price at $30, the average
attendance at recent games has been 27,000. A market survey shows that for every dollar that the ticket
price is lowered, average attendance increases by 3,000.
a) Find a function that models the revenue.
b) What ticket price would be so high that no revenue is generated?
c) Find the price that maximizes revenue from the ticket sales.
6. Find the average rate of change of each function on the given interval.
a.) 𝑓(𝑥) = 𝑥 5 + 2𝑥 4 + 3𝑥 − 12; [−5, −1]
b.) 𝑓(𝑥) =
𝑥−3
𝑥
Section 1.5: Parent Functions and Transformations
1. For the functions below: a) identify the parent, b) list the transformations in the proper order c) graph the
function including at least 3 key points.
−1
a.) 𝑓(𝑥) = 𝑥+2 − 3
b.) 𝑓(𝑥) = 2√−𝑥 − 1
13
c.) 𝑓(𝑥) = 2(−2𝑥 + 6)3 − 1
d.) 𝑓(𝑥) = − 2 √4 − 𝑥
2. Using 𝑓(𝑥) = |𝑥| as the parent function, write the resulting function if the graph is reflected over the xaxis, horizontally shrunk by 3 and moved to the left 6.
y
3. Given the graphs below write the function.
y
a.
b.


x
x


4. Use function notation to represent the following transformations:
a.) Reflection over the x-axis, horizontal stretch of 3, translation to the right 9 and down 4.
b.) Reflection over the y-axis, vertical shrink of 1/4, translation left 2 units and up 6 units.
Make sure you are comfortable describing transformations, finding key points on your graphs, using
function notation to represent transformations and all of the practice we used in class*
Section 1.6: Function Operations and Composition
1
𝑓
1. Given 𝑓(𝑥) = 𝑥+2 and 𝑔(𝑥) = 3𝑥 find: a.) (𝑓 − 𝑔)(𝑥) b.) (𝑔) (𝑥) and the domain for each.
2. Given the functions below find ( f
g )  x  and the domain.
a.) 𝑓(𝑥) = 𝑥 2 + 2, 𝑔(𝑥) = 𝑥 − 3
1
b.) 𝑓(𝑥) = 𝑥 2 −16, 𝑔(𝑥) = 𝑥 + 4
c.) 𝑓(𝑥) = 𝑥 2 − 7, 𝑔(𝑥) = √2𝑥 + 3
4
3. The volume of a spherical weather balloon with radius r is given by 𝑉(𝑟) = 3 𝜋𝑟 3. The balloon is being
inflated so that the radius increases at a constant rate 𝑟(𝑡) = .5𝑡 + 2, where r is in meters and t is the
number of seconds since inflation began.
a.) Find V(r(t))
b.) Find the volume after 10 seconds of inflation.
5. Last weekend you bought a new shed at the local hardware store, unfortunately the shed is too big to fit
into your car. For a small fee, you arrange to have the store deliver your purchase for you. The sales
tax on the purchase is 7.5%, the delivery fee is $30.00.
a.) If x represents the total cost. Write a function t(x) for the total only after taxes. Write a separate function
d(x), for just the total and the delivery fee.
b.) Calculate (t d )  x and (d t )  x  and interpret what they mean.
c.) Suppose taxes by law are not charged on delivery fees; what function should be used?
1
6. Find two functions f(x)and g(x) such that h(x)=(𝑥−7)2
Section 1.7: Inverse Relations and Functions
1. Given a graph, describe two ways you could graph the inverse relation. How can you tell if a function
has an inverse function?
2. Determine whether the function has an inverse, if so, find the inverse and state the domain.
a.) 𝑓(𝑥) = √𝑥 + 7
𝑥+4
c.) 𝑓(𝑥) = |𝑥 − 2| + 5
b.)𝑓(𝑥) = 3𝑥−5
3. Show algebraically that f and g are inverses.
a.) 𝑓(𝑥) = 4𝑥 + 9, 𝑔(𝑥) =
𝑥−9
4
b.) 𝑓(𝑥) =
𝑥2
4
+ 8, 𝑥 ≥ 0 , 𝑔(𝑥) = √4𝑥 − 32