Name:_______________________________________________ Date:___________________
Precalculus (Semester)
Fall 2023
Ms. McGuinness
80 points total- 20 Qs
Precalculus Final Exam (80 pts)
#1) Make a table for the following
function. Then, fill in the graph to the
right, using your table. (4 pts.)
𝑓(𝑥) =
3𝑥 + 10
x
f(x)
-10/3
-3
-2
2
5
13
#2) Identify whether each of the following graphs represent a one-to-one function or not.
Justify your reasoning for each. (2 pts. each - 4 pts. total)
a)
b)
#3) Write the following in interval notation: (1 pt. each- 4 pts. total)
a) All numbers greater than 5
c) − 2 ≤ 𝑥 ≤ 5
b) From negative infinity to -2, including -2 d)
#4) Make a function that has a: (4 pts.)
● Domain of [-4, 3)
● Range of [-6, 5]
on the graph to the right.
#5) Refer to the following piecewise function and
identify whether or not f(x) is continuous at x= 2
through finding the left and right-handed limits of
the function. If it is discontinuous, name what
type of discontinuity is represented and where. (4
pts.)
#6) Refer to the graph of f(x) to the right to answer the following questions. (0.5 pts
each- 4 pts.total)
=
=
#7) Refer to the graph to the right to answer the
following. (4 pts.) Express the domain and range in
interval notation.
a) X-vals of discontinuities:
b) Y-vals of discontinuities:
c) Domain:
d) Range:
#8) Evaluate the following limits using algebraic methods. If no limit exists, write DNE
(does not exist). (4 pts. total)
a)
b)
c)
#9) Refer to the function: f(x) below to answer the following questions.
3
𝑓(𝑥) = (𝑥 + 2) + 3
a) Identify the parent function from the transformed function: f(x). (2 pts.)
b) Identify all of the transformations needed to get from the parent function to the
transformed function: f(x). (2 pts.)
#10) Evaluate the following. (1 pt. each- 4 pts. total)
𝑓(𝑥) =
𝑥 − 3+ 3
2
𝑝(𝑥) = |13 − 𝑥 |
a) 𝑓(19)
b) 𝑝(− 3)
b) 𝑝(5)
d) 𝑓(3)
#11) Refer to the following three functions j, k, and l. Evaluate the following below. (2 pt.
each- 4 pts. total)
2
𝑗(𝑥) = 𝑥 + 2𝑥 − 1
a) (𝑗 + 𝑘)(3)
3
𝑘(𝑥) = 𝑥 − 5
𝑙(𝑥) = 𝑥 + 4
b) (𝑗 ◦ 𝑙)(8)
#12) Decompose the composite function: ℎ(𝑥) =
1
2
(𝑥−2)
into f(x) and g(x) such that:
ℎ(𝑥) = 𝑓(𝑔(𝑥)). (4 pts.)
#13) Do the notations: (𝑓 ◦ 𝑔)(𝑥) and (𝑓 • 𝑔)(𝑥) mean the same thing? Explain briefly.
(4 pts.)
#14) Jon claims that f(x) and g(x) are inverse functions. Thomas claims that they are
not. Who is correct? Show all work using algebra to support your answer. (4 pts.)
3
𝑓(𝑥) = 𝑥 + 2
3
𝑔(𝑥) = (𝑥 − 2)
#15) Divide using either long division or synthetic division. Show all work. Write your
answer as an expression (4 pts.)
3
2
(3𝑥 + 2𝑥 − 37𝑥 + 12) ÷ (𝑥 + 4)
#16) Use the remainder theorem to evaluate f(x) at c. (4 pts.)
4
3
𝑓(𝑥) = 2𝑥 + 4𝑥 + 2𝑥 − 1; 𝑐 =
−2
#17) Use the rational zeros theorem to list all possible rational zeros. (4 pts.)
3
2
𝑓(𝑥) = 𝑥 + 11𝑥 − 15𝑥 − 27
Use the following function for #18 and #19.
2
𝑓(𝑥) =
𝑥 −2𝑥−15
𝑥+3
#18) Does the graph of the above rational function f(x) have a hole? If so, identify where
it is.(4 pts)
#19) Does the graph of the above function f(x) have a slant asymptote? If so, find it! (4
pts.)
#20) Use the factor theorem to determine if the following binomial is a factor of the given
polynomial. If so, completely factor the polynomial and give the zeroes. (4 pts.)
3
2
𝑓(𝑥) = 𝑥 + 6𝑥 − 16𝑥 − 96; (𝑥 − 4)