Question 1

Make a rough sketch of the graph of y = 2 + log $2$ (x + 1). Do not use a calculator. Instead, start with the graph of a simple function and apply any needed transformations.

Accepted Answer

The answer of Make a rough sketch of the graph...

Question 2

The following are the winning times for the Olympic Men's 110 Meter Hurdles:
$$\begin{array}{l}
\begin{array} { | l | l | } 
\hline \text { Year } & \text { Time } \
\hline 1896 & 17.6 \
\hline 1900 & 15.4 \
\hline 1904 & 16 \
\hline 1906 & 16.2 \
\hline 1908 & 15 \
\hline 1912 & 15.1 \
\hline 1920 & 14.8 \
\hline 1924 & 15 \
\hline 1928 & 14.8 \
\hline
\end{array}&\
\begin{array} { | l | l | } 
\hline \text { Year } & \text { Time } \
\hline 1932 & 14.6 \
\hline 1936 & 14.2 \
\hline 1948 & 13.9 \
\hline 1952 & 13.7 \
\hline 1956 & 13.5 \
\hline 1960 & 13.8 \
\hline 1964 & 13.6 \
\hline 1968 & 13.3 \
\hline 1972 & 13.24 \
\hline
\end{array}&
\begin{array} { | l | l | } 
\hline \text { Year } & \text { Time } \
\hline 1976 & 13.3 \
\hline 1980 & 13.39 \
\hline 1984 & 13.2 \
\hline 1988 & 12.98 \
\hline 1992 & 13.12 \
\hline 1996 & 12.95 \
\hline 2000 & 13 \
\hline 2004 & 12.91 \
\hline
\end{array}
\end{array}$$
(a) Make a scatter plot of these data.(b) Fit a linear model to the data.(c) Fit an exponential model to the data
(d) Fit a quadratic model to the data.(e) Use your equations to make a table showing the predicted winning time for each model for the 2008 Olympics, rounded to the nearest hundredth of a second.(f) The actual time for the 2008 Olympics was 12.93 seconds. Which model was closest? Which model was second-closest?

Accepted Answer

(a) @#IMG-DLM& (b) y = -0.0320057x + 76.595
(c) y

Question 3

Find the value of ln e $e$ .

Accepted Answer

A)  $- 1$ 
B)  $1 / \sqrt { e }$ 
C) e 
D) 0 
E)  $\sqrt { e }$ 
F)1/e
G)1
H) - e 
A)  $- 1$ 
B)  $1 / \sqrt { e }$ 
C) e 
D) 0 
E)  $\sqrt { e }$ 
F)1/e
G)1
H) - e

Question 4

Make a rough sketch of the graph of y = 2 + log $3$ (x + 1). Do not use a calculator. Instead, start with the graph of a simple function and apply any needed transformations.

Accepted Answer

The answer of Make a rough sketch of the graph...

Question 5

A bacteria culture starts with 200 bacteria and triples in size every ten minutes. After 1 hour, how many bacteria are there?

Accepted Answer

A) 1800 
B) 3600 
C) 5400 
D) 16,200 
E) 48,600
F)145,800
G)437,400
H)1,312,200 
A) 1800 
B) 3600 
C) 5400 
D) 16,200 
E) 48,600
F)145,800
G)437,400
H)1,312,200

Question 6

The following table defines the function f (x). From this table, write a table for f $- 1$ : Determine the domain for f $- 1$ . $\begin{array} { | c | r | r | r | r | r | r | r | } 
\hline x & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
\hline f ( x ) & - 4 & 5 & 3 & - 2 & 6 & - 5 & 0 \
\hline
\end{array}$

Accepted Answer

@#IMG-DLM& Domain of

Question 7

Classify the function f(x) = sin (5) x $2$ $+$ sin (3) x.

Accepted Answer

A) Power function 
B) Root function 
C) Polynomial function 
D) Rational function 
E) Algebraic function
F)Trigonometric function
G)Exponential function
H)Logarithmic function 
A) Power function 
B) Root function 
C) Polynomial function 
D) Rational function 
E) Algebraic function
F)Trigonometric function
G)Exponential function
H)Logarithmic function

Question 8

Make a rough sketch of the graph of y = 4 $1 - \frac { x } { 2 }$ + 1. Do not use a calculator.

Accepted Answer

The answer of Make a rough sketch of the graph...

Question 9

Suppose that the number of bacteria in a culture at time t is given by $x = 5 ^ { 4 } e ^ { 3 t }$ Use natural logarithms to solve for t in terms of x.

Accepted Answer

The answer of Suppose that the number of bacteria in...

Question 10

A small model rocket is launched vertically upward on a calm day. The engine delivers its
thrust at a constant rate for 2 seconds, at which point the engine burns out. The rocket continues until it begins to fall from its maximum height of 600 feet. Six seconds into the flight a parachute is automatically deployed and the rocket descends at a constant rate of 30 feet per second. Sketch a possible graph of the altitude, h(t), of the rocket at time t for the first 10 seconds of the flight.

Accepted Answer

Answers wi

Question 11

At how many places does the curve x = cos 3t, y = sin t cross the x-axis?

Accepted Answer

A) 1 
B) 2 
C) 3 
D) 4 
E) 5
F)6
G)7
H)8 
A) 1 
B) 2 
C) 3 
D) 4 
E) 5
F)6
G)7
H)8

Question 12

What single transformation of the graph of y = e $x$ is the same as shifting the graph of y = e $x$ four units downward and then reflecting the shifted graph in the x-axis?

Accepted Answer

Reflecting

Question 13

f and g are functions defined by the following table.$$\begin{array} { | l | c | c | c | c | c | c | c | } 
\hline x &-3&-2&-1&0&1&2&3 \
\hline f ( x ) &-5&-4&-3&-2&-1&-2&-3 \
\hline g ( x ) & - 4 & 1 &-1&-2&-1&1&4\
\hline
\end{array}$$
Determine the following:
(a) (f $+$ g)(2)
(b) (f - g)( - 1)
(c) $( f \cdot g ) ( 0 )$ (d) $( f / g ) ( 3 )$ (e) $( f \circ g ) ( - 2 )$ (f) $( f \circ f ) ( 0 )$ (g) $( g \circ f ) ( - 1 )$ (h) $( g \circ g ) ( - 2 )$

Accepted Answer

(a) @#IMG-DLM& 1
(b) @#IMG-DLM& 2
(c) 4

Question 14

Find the inverse of f (x) $= \frac { x + 1 } { 2 - x }$ .

Accepted Answer

The answer of Find the inverse of f (x) \(=...

Question 15

Solve the equation $e ^ { 2 - 3 x } = 125$ .

Accepted Answer

A)  $x = 2 - \ln 5$ 
B)  $x = 2 - 3 \ln 5$ 
C)  $x = \frac { 2 } { 3 } - \ln 5$ 
D)  $x = \frac { 2 } { 3 } - 3 \ln 5$ 
E)  $x = - \ln 5$ 
F) $x = - \frac { 1 } { 3 } \ln 5$ 
G) $x = \frac { 2 } { 3 } \ln 5$ 
H) $x = 2 + 3 \ln 5$ 
A)  $x = 2 - \ln 5$ 
B)  $x = 2 - 3 \ln 5$ 
C)  $x = \frac { 2 } { 3 } - \ln 5$ 
D)  $x = \frac { 2 } { 3 } - 3 \ln 5$ 
E)  $x = - \ln 5$ 
F) $x = - \frac { 1 } { 3 } \ln 5$ 
G) $x = \frac { 2 } { 3 } \ln 5$ 
H) $x = 2 + 3 \ln 5$

Question 16

Determine whether or not the function f (x) = x $2$ - 2x + 5 is one-to-one.

Accepted Answer

f is not o

Question 17

Let f (x) = $\sqrt { 2 x + 5 }$ . Find each of the following:
(a) f (0) $+$ f ( $- 2$ )
(b) f (x $+$ 2)
(c) [f (x)] $2$ (d) f (x $2$ )

Accepted Answer

(a) f (0) @#IMG-DLM& f ( @#IMG-DLM& ) =

Question 18

A parking lot light is mounted on top of a 20-foot tall lamppost. A person T feet tall is
walking away from the lamppost along a straight path. Determine a function which expresses
the length of the person's shadow in terms of the person's distance from the lamppost.

Accepted Answer

Let L be the length of the per

Question 19

Find the difference between the largest and smallest solutions of the equation - 3x $2$ - 9x = 2 $x$ , rounded to two decimal places.

Accepted Answer

A) 0.02 
B) 0.23 
C) 0.80 
D) 1.05 
E) 2.06
F)2.88
G)3.09
H)3.92 
A) 0.02 
B) 0.23 
C) 0.80 
D) 1.05 
E) 2.06
F)2.88
G)3.09
H)3.92

Question 20

Let f (x) = $\left\{ \begin{array} { l l } 
x ^ { 2 } + 3 & \text { if } x \leq - 1 \
\frac { 2 + 3 x } { 6 } & \text { if } x > - 1
\end{array} \right.$ (a) the domain of f.(b) the range of f.

Accepted Answer

The answer of Let f (x) = \(\left\{ \begin{array} {...

Make a rough sketch of the graph of y = 2 + log $2$ (x + 1). Do not use a calculator. Instead, start with the graph of a simple function and apply any needed transformations.

Find the value of ln e $e$ .

Make a rough sketch of the graph of y = 2 + log $3$ (x + 1). Do not use a calculator. Instead, start with the graph of a simple function and apply any needed transformations.

A bacteria culture starts with 200 bacteria and triples in size every ten minutes. After 1 hour, how many bacteria are there?

The following table defines the function f (x). From this table, write a table for f $- 1$ : Determine the domain for f $- 1$ . x 1 2 3 4 5 6 7 f(x) -4 5 3 -2 6 -5 0

Classify the function f(x) = sin (5) x $2$ $+$ sin (3) x.

Make a rough sketch of the graph of y = 4 $1 - \frac { x } { 2 }$ + 1. Do not use a calculator.

Suppose that the number of bacteria in a culture at time t is given by $x = 5 ^ { 4 } e ^ { 3 t }$ Use natural logarithms to solve for t in terms of x.

At how many places does the curve x = cos 3t, y = sin t cross the x-axis?

What single transformation of the graph of y = e $x$ is the same as shifting the graph of y = e $x$ four units downward and then reflecting the shifted graph in the x-axis?

Find the inverse of f (x) $= \frac { x + 1 } { 2 - x }$ .

Solve the equation $e ^ { 2 - 3 x } = 125$ .

Determine whether or not the function f (x) = x $2$ - 2x + 5 is one-to-one.

Let f (x) = $\sqrt { 2 x + 5 }$ . Find each of the following: (a) f (0) $+$ f ( $- 2$ ) (b) f (x $+$ 2) (c) [f (x)] $2$ (d) f (x $2$ )

A parking lot light is mounted on top of a 20-foot tall lamppost. A person T feet tall is walking away from the lamppost along a straight path. Determine a function which expresses the length of the person's shadow in terms of the person's distance from the lamppost.

Find the difference between the largest and smallest solutions of the equation - 3x $2$ - 9x = 2 $x$ , rounded to two decimal places.

Let f (x) = $\left\{ \begin{array} { l l } x ^ { 2 } + 3 & \text { if } x \leq - 1 \\\frac { 2 + 3 x } { 6 } & \text { if } x > - 1\end{array} \right.$ (a) the domain of f.(b) the range of f.

Limits and Derivatives

Differentiation Rules

Applications of Differentiation

Integrals

Applications of Integration

Differential Equations

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Filters

Exam 1: Functions and Models

Make a rough sketch of the graph of y = 2 + log 222 (x + 1). Do not use a calculator. Instead, start with the graph of a simple function and apply any needed transformations.

Find the value of ln e eee .

Make a rough sketch of the graph of y = 2 + log 333 (x + 1). Do not use a calculator. Instead, start with the graph of a simple function and apply any needed transformations.

A bacteria culture starts with 200 bacteria and triples in size every ten minutes. After 1 hour, how many bacteria are there?

The following table defines the function f (x). From this table, write a table for f −1- 1−1 : Determine the domain for f −1- 1−1 . x 1 2 3 4 5 6 7 f(x) -4 5 3 -2 6 -5 0

Classify the function f(x) = sin (5) x 222 +++ sin (3) x.

Make a rough sketch of the graph of y = 4 1−x21 - \frac { x } { 2 }1−2x​ + 1. Do not use a calculator.

Suppose that the number of bacteria in a culture at time t is given by x=54e3tx = 5 ^ { 4 } e ^ { 3 t }x=54e3t Use natural logarithms to solve for t in terms of x.

At how many places does the curve x = cos 3t, y = sin t cross the x-axis?

What single transformation of the graph of y = e xxx is the same as shifting the graph of y = e xxx four units downward and then reflecting the shifted graph in the x-axis?

Find the inverse of f (x) =x+12−x= \frac { x + 1 } { 2 - x }=2−xx+1​ .

Solve the equation e2−3x=125e ^ { 2 - 3 x } = 125e2−3x=125 .

Determine whether or not the function f (x) = x 222 - 2x + 5 is one-to-one.

Let f (x) = 2x+5\sqrt { 2 x + 5 }2x+5​ . Find each of the following: (a) f (0) +++ f ( −2- 2−2 ) (b) f (x +++ 2) (c) [f (x)] 222 (d) f (x 222 )

A parking lot light is mounted on top of a 20-foot tall lamppost. A person T feet tall is walking away from the lamppost along a straight path. Determine a function which expresses the length of the person's shadow in terms of the person's distance from the lamppost.

Find the difference between the largest and smallest solutions of the equation - 3x 222 - 9x = 2 xxx , rounded to two decimal places.

Let f (x) = {x2+3 if x≤−12+3x6 if x>−1\left\{ \begin{array} { l l } x ^ { 2 } + 3 & \text { if } x \leq - 1 \\\frac { 2 + 3 x } { 6 } & \text { if } x > - 1\end{array} \right.{x2+362+3x​​ if x≤−1 if x>−1​ (a) the domain of f.(b) the range of f.

Limits and Derivatives

Differentiation Rules

Applications of Differentiation

Integrals

Applications of Integration

Differential Equations

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Filters

Make a rough sketch of the graph of y = 2 + log $2$ (x + 1). Do not use a calculator. Instead, start with the graph of a simple function and apply any needed transformations.

Find the value of ln e $e$ .

Make a rough sketch of the graph of y = 2 + log $3$ (x + 1). Do not use a calculator. Instead, start with the graph of a simple function and apply any needed transformations.

The following table defines the function f (x). From this table, write a table for f $- 1$ : Determine the domain for f $- 1$ . x 1 2 3 4 5 6 7 f(x) -4 5 3 -2 6 -5 0

Classify the function f(x) = sin (5) x $2$ $+$ sin (3) x.

Make a rough sketch of the graph of y = 4 $1 - \frac { x } { 2 }$ + 1. Do not use a calculator.

Suppose that the number of bacteria in a culture at time t is given by $x = 5 ^ { 4 } e ^ { 3 t }$ Use natural logarithms to solve for t in terms of x.

What single transformation of the graph of y = e $x$ is the same as shifting the graph of y = e $x$ four units downward and then reflecting the shifted graph in the x-axis?

Find the inverse of f (x) $= \frac { x + 1 } { 2 - x }$ .

Solve the equation $e ^ { 2 - 3 x } = 125$ .

Determine whether or not the function f (x) = x $2$ - 2x + 5 is one-to-one.

Let f (x) = $\sqrt { 2 x + 5 }$ . Find each of the following: (a) f (0) $+$ f ( $- 2$ ) (b) f (x $+$ 2) (c) [f (x)] $2$ (d) f (x $2$ )

Find the difference between the largest and smallest solutions of the equation - 3x $2$ - 9x = 2 $x$ , rounded to two decimal places.

Let f (x) = $\left\{ \begin{array} { l l } x ^ { 2 } + 3 & \text { if } x \leq - 1 \\\frac { 2 + 3 x } { 6 } & \text { if } x > - 1\end{array} \right.$ (a) the domain of f.(b) the range of f.