Question 1

Relative to the graph of y = e $x$ , the graph of y = $e ^ { x + 5 }$ is changed in what way?

Accepted Answer

A) Shifted 5 units upward 
B) Shifted 5 units downward 
C) Shifted 5 units to the right 
D) Shifted 5 units to the left 
E) Stretched horizontally by a factor of 5
F)Stretched vertically by a factor of 5
G)Compressed horizontally by a factor of 5
H)Compressed vertically by a factor of 5 
A) Shifted 5 units upward 
B) Shifted 5 units downward 
C) Shifted 5 units to the right 
D) Shifted 5 units to the left 
E) Stretched horizontally by a factor of 5
F)Stretched vertically by a factor of 5
G)Compressed horizontally by a factor of 5
H)Compressed vertically by a factor of 5

Question 2

Find the smallest value in the range of the function f (x) = 3x2 + 24x + 40.

Accepted Answer

A)  $- 4$ 
B)  $- 5$ 
C)  $- 6$ 
D)  $- 7$ 
E)  $- 8$ 
F) $- 16$ 
G) $- 24$ 
H) $- 40$ 
A)  $- 4$ 
B)  $- 5$ 
C)  $- 6$ 
D)  $- 7$ 
E)  $- 8$ 
F) $- 16$ 
G) $- 24$ 
H) $- 40$

Question 3

Consider the pairs of parametric equations $x = 2 - 3 t , y = 7 - 6 t$ and $x = t - 1 , y = 1 + 2 t$ (a) Show that these pairs of equations produce the same line.(b) What are the slope and y-intercept of this line?

Accepted Answer

(a) y = 2x

Question 4

Find functions f and g such that F(x) = e $\sin x$ = $( f \circ g ) ( x )$

Accepted Answer

f (x) = e @#IMG-DLM& , g(x) @#IMG-DLM& s

Question 5

Find the value of (4 ln $e ^ { 3 }$ $- e ^ { 2 \ln 3 } +$ 5 ln 1)(ln $\sqrt [ 4 ] { e }$ ).

Accepted Answer

(4 ln @#IMG-DLM& ln

Question 6

Given the graph of y = f(x):   Sketch the graph of each of the following functions:
(a) $- f ( x )$ 
(b) $f ( - x )$ 
(c) $f ^ { \prime } ( 2 x )$ 
(d) $2 f ( x )$ 
(e) $- f ( - x )$ 
(f) $f \left( \frac { 1 } { 2 } x \right)$ 
(g) $\frac { 1 } { 2 } f ( x )$ 
(h) f $( x + 1 )$ 
(i) $f ( x ) -$ 1
(j) 1 $- f ( x )$

Accepted Answer

The answer of Given the graph of y = f(x):...

Question 7

Express the area A of a circle as a function of its circumference C.

Accepted Answer

The answer of Express the area A of a circle...

Question 8

Determine an appropriate viewing rectangle for the graph of the function $f ( x ) = ( x + 50 ) ^ { 2 } + 1000$ .

Accepted Answer

A) [ - 60, - 40] $\times$ [40, 60] 
B) [2400,2600] $\times$ [900, 120] 
C) [40,60] $\times$ [980,1020] 
D) [40,60] $\times$ [ - 1020, - 980] 
E) [40, 60] $\times$ [40, 60]
F)[ - 60, - 40] $\times$ [980, 1020]
G)[ - 10, 10] $\times$ [ - 10, 10]
H)[980, 1020] $\times$ [980, 1020] 
A) [ - 60, - 40] $\times$ [40, 60] 
B) [2400,2600] $\times$ [900, 120] 
C) [40,60] $\times$ [980,1020] 
D) [40,60] $\times$ [ - 1020, - 980] 
E) [40, 60] $\times$ [40, 60]
F)[ - 60, - 40] $\times$ [980, 1020]
G)[ - 10, 10] $\times$ [ - 10, 10]
H)[980, 1020] $\times$ [980, 1020]

Question 9

The radioactive isotope Bismuth-210 has a half-life of 5 days. How many days does it take for 87.5% of a given amount to decay?

Accepted Answer

A) 15 
B) 8 
C) 10 
D) 13 
E) 11
F)9
G)12
H)14 
A) 15 
B) 8 
C) 10 
D) 13 
E) 11
F)9
G)12
H)14

Question 10

Let f (x) = $\sqrt { \frac { 2 } { x + 3 } }$ , x $>$ $- 3$ . Find each of the following:
(a) f ( - 1) - f ( $- 2$ )
(b) f (x $2$ - 3)
(c) f (x $2$ ) - 3
(d) [f (x - 3)] $2$

Accepted Answer

(a) f ( @#IMG-DLM& 1) @#IMG-DLM& f ( @#IMG-DLM& )

Question 11

Find the value of 4 $\log _ { 2 } 3$

Accepted Answer

The answer of Find the value of 4 \(\log _...

Question 12

Find the largest value in the domain of the function $f ( x ) = \sqrt { \frac { 3 - 2 x } { 4 + 3 x } }$ .

Accepted Answer

A)  $- \frac { 3 } { 2 }$ 
B)  $- \frac { 2 } { 3 }$ 
C) 0 
D) 2 
E)  $\frac { 2 } { 3 }$ 
F) $\frac { 3 } { 2 }$ 
G)3
H)No largest value 
A)  $- \frac { 3 } { 2 }$ 
B)  $- \frac { 2 } { 3 }$ 
C) 0 
D) 2 
E)  $\frac { 2 } { 3 }$ 
F) $\frac { 3 } { 2 }$ 
G)3
H)No largest value

Question 13

The half-life of a certain radioactive substance is 5 days. The initial size of a sample is 10 grams.(a) Find the amount of the substance remaining after 20 days.(b) Find the amount of the substance remaining after t days.(c) Use a graph to estimate, to the nearest 0:01 gram, the amount remaining after 14 days.(d) Use the graph to estimate, to the nearest 0:1 day, the amount of time required for the mass of the substance to be reduced to 0:1 gram.

Accepted Answer

(a) The half-life is 5 days, so 20 days

Question 14

Find the inverse function for f (x) = $\frac { 5 - 2 x } { 3 }$ .

Accepted Answer

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

Question 15

Classify the function f(x) = $\frac { x ^ { 2 } + \pi } { x }$

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 16

The range of the function f (x) = $\sqrt { 20 + 8 x - x ^ { 2 } }$ is a closed interval [a; b]. Find its length b - a.

Accepted Answer

A) 1 
B) 2 
C) 3 
D) 4 
E) 5
F)6
G)7
H)9 
A) 1 
B) 2 
C) 3 
D) 4 
E) 5
F)6
G)7
H)9

Question 17

Eliminate the parameter in the equations $x = t ^ { 2 } , y = t ^ { 4 }$

Accepted Answer

A)  $y = x ^ { 2 } \text { for } x \geq 0$ 
B)  $y = \sqrt { x } \text { for } x \geq 0$ 
C)  $y = 2 x ^ { 2 } \text { for } x \geq 0$ 
D)  $y = \sqrt { 2 x } \text { for } x \geq 0$ 
E)  $y = 2 \sqrt { x } \text { for } x \geq 0$ 
F) $y = x ^ { 2 } / 2 \text { for } x \geq 0$ 
G) $y = \sqrt { x } / 2 \text { for } x \geq 0$ 
H) $y = \sqrt { x / 2 } \text { for } x \geq 0$ 
A)  $y = x ^ { 2 } \text { for } x \geq 0$ 
B)  $y = \sqrt { x } \text { for } x \geq 0$ 
C)  $y = 2 x ^ { 2 } \text { for } x \geq 0$ 
D)  $y = \sqrt { 2 x } \text { for } x \geq 0$ 
E)  $y = 2 \sqrt { x } \text { for } x \geq 0$ 
F) $y = x ^ { 2 } / 2 \text { for } x \geq 0$ 
G) $y = \sqrt { x } / 2 \text { for } x \geq 0$ 
H) $y = \sqrt { x / 2 } \text { for } x \geq 0$

Question 18

A bacteria culture starts with 500 bacteria and doubles every 2 hours. How many bacteria are there after 6 hours?

Accepted Answer

A) 1,000 
B) 1,500 
C) 2,000 
D) 2,500 
E) 3,000
F)4,000
G)5,000
H)10,000 
A) 1,000 
B) 1,500 
C) 2,000 
D) 2,500 
E) 3,000
F)4,000
G)5,000
H)10,000

Relative to the graph of y = e $x$ , the graph of y = $e ^ { x + 5 }$ is changed in what way?

Find the smallest value in the range of the function f (x) = 3x² + 24x + 40.

Consider the pairs of parametric equations $x = 2 - 3 t , y = 7 - 6 t$ and $x = t - 1 , y = 1 + 2 t$ (a) Show that these pairs of equations produce the same line.(b) What are the slope and y-intercept of this line?

Find functions f and g such that F(x) = e $\sin x$ = $( f \circ g ) ( x )$

Find the value of (4 ln $e ^ { 3 }$ $- e ^ { 2 \ln 3 } +$ 5 ln 1)(ln $\sqrt [ 4 ] { e }$ ).

Express the area A of a circle as a function of its circumference C.

Determine an appropriate viewing rectangle for the graph of the function $f ( x ) = ( x + 50 ) ^ { 2 } + 1000$ .

The radioactive isotope Bismuth-210 has a half-life of 5 days. How many days does it take for 87.5% of a given amount to decay?

Let f (x) = $\sqrt { \frac { 2 } { x + 3 } }$ , x $>$ $- 3$ . Find each of the following: (a) f ( - 1) - f ( $- 2$ ) (b) f (x $2$ - 3) (c) f (x $2$ ) - 3 (d) [f (x - 3)] $2$

Find the value of 4 $\log _ { 2 } 3$

Find the largest value in the domain of the function $f ( x ) = \sqrt { \frac { 3 - 2 x } { 4 + 3 x } }$ .

Find the inverse function for f (x) = $\frac { 5 - 2 x } { 3 }$ .

Classify the function f(x) = $\frac { x ^ { 2 } + \pi } { x }$

The range of the function f (x) = $\sqrt { 20 + 8 x - x ^ { 2 } }$ is a closed interval [a; b]. Find its length b - a.

Eliminate the parameter in the equations $x = t ^ { 2 } , y = t ^ { 4 }$

A bacteria culture starts with 500 bacteria and doubles every 2 hours. How many bacteria are there after 6 hours?

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

Relative to the graph of y = e xxx , the graph of y = ex+5e ^ { x + 5 }ex+5 is changed in what way?

Find the smallest value in the range of the function f (x) = 3x2 + 24x + 40.

Consider the pairs of parametric equations x=2−3t,y=7−6tx = 2 - 3 t , y = 7 - 6 tx=2−3t,y=7−6t and x=t−1,y=1+2tx = t - 1 , y = 1 + 2 tx=t−1,y=1+2t (a) Show that these pairs of equations produce the same line.(b) What are the slope and y-intercept of this line?

Find functions f and g such that F(x) = e sin⁡x\sin xsinx = (f∘g)(x)( f \circ g ) ( x )(f∘g)(x)

Find the value of (4 ln e3e ^ { 3 }e3 −e2ln⁡3+- e ^ { 2 \ln 3 } +−e2ln3+ 5 ln 1)(ln e4\sqrt [ 4 ] { e }4e​ ).

Express the area A of a circle as a function of its circumference C.

Determine an appropriate viewing rectangle for the graph of the function f(x)=(x+50)2+1000f ( x ) = ( x + 50 ) ^ { 2 } + 1000f(x)=(x+50)2+1000 .

The radioactive isotope Bismuth-210 has a half-life of 5 days. How many days does it take for 87.5% of a given amount to decay?

Let f (x) = 2x+3\sqrt { \frac { 2 } { x + 3 } }x+32​​ , x >>> −3- 3−3 . Find each of the following: (a) f ( - 1) - f ( −2- 2−2 ) (b) f (x 222 - 3) (c) f (x 222 ) - 3 (d) [f (x - 3)] 222

Find the value of 4 log⁡23\log _ { 2 } 3log2​3

Find the largest value in the domain of the function f(x)=3−2x4+3xf ( x ) = \sqrt { \frac { 3 - 2 x } { 4 + 3 x } }f(x)=4+3x3−2x​​ .

Find the inverse function for f (x) = 5−2x3\frac { 5 - 2 x } { 3 }35−2x​ .

Classify the function f(x) = x2+πx\frac { x ^ { 2 } + \pi } { x }xx2+π​

The range of the function f (x) = 20+8x−x2\sqrt { 20 + 8 x - x ^ { 2 } }20+8x−x2​ is a closed interval [a; b]. Find its length b - a.

Eliminate the parameter in the equations x=t2,y=t4x = t ^ { 2 } , y = t ^ { 4 }x=t2,y=t4

A bacteria culture starts with 500 bacteria and doubles every 2 hours. How many bacteria are there after 6 hours?

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

Relative to the graph of y = e $x$ , the graph of y = $e ^ { x + 5 }$ is changed in what way?

Find the smallest value in the range of the function f (x) = 3x² + 24x + 40.

Consider the pairs of parametric equations $x = 2 - 3 t , y = 7 - 6 t$ and $x = t - 1 , y = 1 + 2 t$ (a) Show that these pairs of equations produce the same line.(b) What are the slope and y-intercept of this line?

Find functions f and g such that F(x) = e $\sin x$ = $( f \circ g ) ( x )$

Find the value of (4 ln $e ^ { 3 }$ $- e ^ { 2 \ln 3 } +$ 5 ln 1)(ln $\sqrt [ 4 ] { e }$ ).

Determine an appropriate viewing rectangle for the graph of the function $f ( x ) = ( x + 50 ) ^ { 2 } + 1000$ .

Let f (x) = $\sqrt { \frac { 2 } { x + 3 } }$ , x $>$ $- 3$ . Find each of the following: (a) f ( - 1) - f ( $- 2$ ) (b) f (x $2$ - 3) (c) f (x $2$ ) - 3 (d) [f (x - 3)] $2$

Find the value of 4 $\log _ { 2 } 3$

Find the largest value in the domain of the function $f ( x ) = \sqrt { \frac { 3 - 2 x } { 4 + 3 x } }$ .

Find the inverse function for f (x) = $\frac { 5 - 2 x } { 3 }$ .

Classify the function f(x) = $\frac { x ^ { 2 } + \pi } { x }$

The range of the function f (x) = $\sqrt { 20 + 8 x - x ^ { 2 } }$ is a closed interval [a; b]. Find its length b - a.

Eliminate the parameter in the equations $x = t ^ { 2 } , y = t ^ { 4 }$