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

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) $- 40$

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

The answer of Consider the pairs of parametric equations \(x...

Question 4

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

Accepted Answer

The answer of Find functions f and g such that...

Question 5

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

Accepted Answer

The answer of Find the value of (4 ln \(e...

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]

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

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

The answer of Let f (x) = \(\sqrt { \frac...

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

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

The answer of The half-life of a certain radioactive substance...

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) $3 x - 5$

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

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

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) $y = \sqrt { x / 2 } \text { for } x \geq 0$

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

Exam 1: Functions and Models

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?

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?

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 $x = t ^ { 2 } , y = t ^ { 4 }$