# 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

m_{0} 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:

2y^{2} − 9x^{2} −18 = 0

**Graphing and Translations
**91. Determine the correct function for the given

graph.

(a) f (x) = 2x^{3} − 3x^{2}

(b) f (x) = 3x^{4} − 2x^{3}

(c) f (x) = 2x^{3} + 3x^{2}

(d) f (x) = 3x^{2} − 2x^{3}

(e)None of these

92. Sketch the graph of the following

function:

93. Graph the following function:

f (x) = 4x^{2} −8x + 4

94. Use the graph of y = x^{4} 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) = x^{2} ?

**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) = −x^{2} + 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) = x^{2} + 4 .

115. Evaluate ( f o g)(3)where

and g(x) = x^{2} +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. i^{2} + 3i + 2

128. i^{3} − 2i^{2} + 4i − 3

129. i^{4} + 4i^{3} −12i^{2} −13i +1

Find the conjugate of the following complex

numbers: