Math 119 Pretest Review Questions
80. Write as the logarithm of a single quantity:
2ln|3x| + ln|x +1| − 3ln|y|
Simplify:
85. The spread of a flu virus through a certain
population is modeled by
where y is the total number infected after t days. In
how many days will 820 people be infected with the
virus?
86. The amount remaining of a decaying sample is
described by the function
where
m0 is the initial amount, t is the number of hours,
and h is the sample’s half-life. Given an isotope of
sodium with a half-life of 15 hours, find the amount
remaining from a 2 g. sample after 20 hours.
87. The number of bacteria in a culture is given by
the formula
What is the half-life for this type of bacteria?
Conic Sections
88. Find the standard equation of the parabola with
vertex at (0,0) and directrix x = 7
89. Find the standard equation of the ellipse with
center at (0,0) a focus at
and minor axis
of length 4.
90. Find the foci of the hyperbola:
2y2 − 9x2 −18 = 0
Graphing and Translations
91. Determine the correct function for the given
graph.
(a) f (x) = 2x3 − 3x2
(b) f (x) = 3x4 − 2x3
(c) f (x) = 2x3 + 3x2
(d) f (x) = 3x2 − 2x3
(e)None of these
92. Sketch the graph of the following
function:
93. Graph the following function:
f (x) = 4x2 −8x + 4
94. Use the graph of y = x4 to find a formula for the
function y = f (x) .
95. Given the graph of
, graph
96. What sequence of transformations will yield the
graph of g(x) = (x +1)2 +10 from the graph of
f (x) = x2 ?
Domain
Determine the domain of the function:
Asymptotes
100. Graph the following function:
101. Graph the following rational function:
102. Match the graph with the correct function.
(e) None of these
End Behavior
Describe the end behavior of the following functions:
Vertical and Horizontal Line Tests
106. Use the vertical line test to determine in which
case y is a function of x .
107. Which of the following graphs represent y as a
function of x ?
One-to-One Functions
Determine whether each function is one-to-one. If it
is, find its inverse.
Inverse functions
Find the inverse of the following functions. State the
domain and range of f -1 (x) .
110. f (x) = −x2 + 3, for x ≥ 0
111.
, for x ≥ 0
112.
, for 0 ≤ x ≤ 5
Composition of Functions
113. Evaluate ( f o g)(2) where
f (x) = 4x and g(x) = −2x +1.
114. Evaluate ( f o g)(3)where
f (x) = −3x + 7 and g(x) = x2 + 4 .
115. Evaluate ( f o g)(3)where
and g(x) = x2 +1.
Partial Fraction Decomposition
Find the partial fraction decomposition for the
following expressions:
Sequences and Series
119. Write the first five terms of the geometric
sequence with
and
120. Find the eighth term of the arithmetic sequence
with
and d = 8 . (Assume that n begins with
1.)
121. Determine whether the following is a geometric
series, if so, find r: -2, 4, -8, 16, -32…
Probability
122. The flags of seven different countries are to be
displayed in a row. In how many different orders can
they be flown?
123. Nine candidates are participating in an election.
In how many different orders can they finish?
124. There are eight football teams in the Mountain
West Conference. In how many different orders can
these eight teams finish in the final rankings?
125. Six friends are driving to a basketball game. In
how many different orders can they arrive?
126. A box holds 12 white, 5 red, and 6 black
marbles. If 2 marbles are picked at random, without
replacement, what is the probability that they will
both be black?
Complex Numbers
Simplify the following complex numbers:
127. i2 + 3i + 2
128. i3 − 2i2 + 4i − 3
129. i4 + 4i3 −12i2 −13i +1
Find the conjugate of the following complex
numbers:
