Question 1

Express the given function as a composite of functions f and g such that y = f(g(x)).
-$y = ( 8 x - 19 ) ^ { 4 }$

Accepted Answer

A)  $f ( x ) = ( 8 x ) ^ { 4 } , g ( x ) = - 19$ 
B)  $f ( x ) = 8 x - 19 , g ( x ) = x ^ { 4 }$ 
C)  $f ( x ) = x ^ { 4 } , g ( x ) = 8 x - 19$ 
D)  $f ( x ) = 8 x ^ { 4 } , g ( x ) = x - 19$ 
A)  $f ( x ) = ( 8 x ) ^ { 4 } , g ( x ) = - 19$ 
B)  $f ( x ) = 8 x - 19 , g ( x ) = x ^ { 4 }$ 
C)  $f ( x ) = x ^ { 4 } , g ( x ) = 8 x - 19$ 
D)  $f ( x ) = 8 x ^ { 4 } , g ( x ) = x - 19$

Question 2

Determine if the function is even, odd, or neither.
-$f ( x ) = 3 x ^ { 2 } + 2$

Accepted Answer

A)  Even 
B)  Odd 
C)  Neither 
A)  Even 
B)  Odd 
C)  Neither

Question 3

Find the domain and range of the function.
-$$F ( t ) = \frac { 6 } { \sqrt { t } }$$

Accepted Answer

A)  D: $( - \infty , \infty ) , R : ( - \infty , \infty )$ 
B)  D: $[ 0 , \infty ) , \mathrm { R } : ( - \infty , \infty )$ 
C)  D: $( - \infty , 0 ) , \mathrm { R } : ( - \infty , 0 )$ 
D)  D: $( 0 , \infty ) , \mathrm { R } : ( 0 , \infty )$ 
A)  D: $( - \infty , \infty ) , R : ( - \infty , \infty )$ 
B)  D: $[ 0 , \infty ) , \mathrm { R } : ( - \infty , \infty )$ 
C)  D: $( - \infty , 0 ) , \mathrm { R } : ( - \infty , 0 )$ 
D)  D: $( 0 , \infty ) , \mathrm { R } : ( 0 , \infty )$

Question 4

Express the given function as a composite of functions f and g such that y = f(g(x)).
-$y = \frac { 1 } { x ^ { 2 } - 7 }$

Accepted Answer

A)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = x - 7$ 
B)  $f ( x ) = \frac { 1 } { x } , g ( x ) = x ^ { 2 } - 7$ 
C)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = - \frac { 1 } { 7 }$ 
D)  $f ( x ) = \frac { 1 } { 7 } , g ( x ) = x ^ { 2 } - 7$ 
A)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = x - 7$ 
B)  $f ( x ) = \frac { 1 } { x } , g ( x ) = x ^ { 2 } - 7$ 
C)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = - \frac { 1 } { 7 }$ 
D)  $f ( x ) = \frac { 1 } { 7 } , g ( x ) = x ^ { 2 } - 7$

Question 5

Find the domain and graph the function.
-f(x) = 4x + 9

Accepted Answer

A)  D: $( - \infty , \infty )$
  
B)  D: $( - \infty , \infty )$
  
C)  D: $[ 0 , \infty )$
  
D)  D: $( - \infty , \infty )$
  
A)  D: $( - \infty , \infty )$
  
B)  D: $( - \infty , \infty )$
  
C)  D: $[ 0 , \infty )$
  
D)  D: $( - \infty , \infty )$

Question 6

Determine if the function is even, odd, or neither.
-$$f ( x ) = \frac { 5 } { x + 9 }$$

Accepted Answer

A)  Even 
B)  Odd 
C)  Neither 
A)  Even 
B)  Odd 
C)  Neither

Question 7

Find the domain and range for the indicated function.
-$f ( x ) = \sqrt { x + 11 } , \quad g ( x ) = \sqrt { x - 11 }$
$\mathrm { f } - \mathrm { g }$

Accepted Answer

A)  D: $x \geq 11$
R: $y \geq 0$ 
B)  D: $x \geq - 11$
$R : y \geq \sqrt { 22 }$ 
C)  D: $x \geq 11$
R: $y \geq \sqrt { 22 }$ 
D)  D: $x \geq - 11$
R: $y \geq 0$ 
A)  D: $x \geq 11$
R: $y \geq 0$ 
B)  D: $x \geq - 11$
$R : y \geq \sqrt { 22 }$ 
C)  D: $x \geq 11$
R: $y \geq \sqrt { 22 }$ 
D)  D: $x \geq - 11$
R: $y \geq 0$

Question 8

Graph the function.
-$$f ( x ) = \left\{ \begin{array} { l l } 
4 x + 2 , & x  3
\end{array} \right.$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 9

Express the given function as a composite of functions f and g such that y = f(g(x)).
-Let $g ( x ) = x + 8$. Find a function $y = f ( x )$ so that $( f \circ g ) ( x ) = 3 x + 24$

Accepted Answer

A)  $f ( x ) = 3 x + 8$ 
B)  $f ( x ) = 3 ( x + 1 )$ 
C)  $f ( x ) = 3 x - 8$ 
D)  $f ( x ) = 3 x$ 
A)  $f ( x ) = 3 x + 8$ 
B)  $f ( x ) = 3 ( x + 1 )$ 
C)  $f ( x ) = 3 x - 8$ 
D)  $f ( x ) = 3 x$

Question 10

Express the given function as a composite of functions f and g such that y = f(g(x)).
-$y = | 4 x + 10 |$

Accepted Answer

A)  $f ( x ) = | - x | , g ( x ) = 4 x - 10$ 
B)  $f ( x ) = - | x | , g ( x ) = 4 x + 10$ 
C)  $f ( x ) = x , g ( x ) = 4 x + 10$ 
D)  $f ( x ) = | x | , g ( x ) = 4 x + 10$ 
A)  $f ( x ) = | - x | , g ( x ) = 4 x - 10$ 
B)  $f ( x ) = - | x | , g ( x ) = 4 x + 10$ 
C)  $f ( x ) = x , g ( x ) = 4 x + 10$ 
D)  $f ( x ) = | x | , g ( x ) = 4 x + 10$

Question 11

Provide an appropriate response.
-$\text { Consider the function } y = \sqrt { 1 - \frac { 1 } { x } } . \text { Can } x \text { be greater than } 0 \text {, but less than } 1 \text { ? }$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 12

Determine whether or not the graph is a graph of a function of x.
-

Accepted Answer

A)  Function 
B)  Not a function 
A)  Function 
B)  Not a function

Question 13

Find the domain and graph the function.
-$F ( t ) = \frac { | t - 1 | } { t - 1 }$

Accepted Answer

A)  D: $( - \infty , 1 ) \cup ( 1 > , \infty )$
  
B)  D: $( - \infty , 1 ) \cup ( 1 , \infty )$
  
C)  D: $( - \infty , \infty )$
  
D)  D: $( - \infty , 0 ) \cup ( 0 , \infty )$
  
A)  D: $( - \infty , 1 ) \cup ( 1 > , \infty )$
  
B)  D: $( - \infty , 1 ) \cup ( 1 , \infty )$
  
C)  D: $( - \infty , \infty )$
  
D)  D: $( - \infty , 0 ) \cup ( 0 , \infty )$

Question 14

Graph the function.
-$f ( x ) = \left\{ \begin{array} { l l } 
- 2 - x , & x < 1 \
1 , & x \geq 1
\end{array} \right.$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 15

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 inches by 29 inches by cutting out equal squares of side x at each corner and then folding up the sides as in the figure.
Express the volume V of the box as a function of x.

Accepted Answer

A)  V(x) = x(12 - x)(29 - x) 
B)  V(x) = (12 - x)(29 - x) 
C)  V(x) = (12 - 2x)(29 - 2x) 
D)  V(x) = x(12 - 2x)(29 - 2x) 
A)  V(x) = x(12 - x)(29 - x) 
B)  V(x) = (12 - x)(29 - x) 
C)  V(x) = (12 - 2x)(29 - 2x) 
D)  V(x) = x(12 - 2x)(29 - 2x)

Question 16

Find the domain and range of the function.
-$$g ( z ) = - 2 - \sqrt { z }$$

Accepted Answer

A)  D: $( - \infty , 0 ]$, R: $[ - 2 , \infty )$ 
B)  D: $( - \infty , \infty ) , \mathrm { R } : ( - \infty , - 2 ]$ 
C)  D: $[ 0 , \infty ) , \mathrm { R } : ( - \infty , - 2 ]$ 
D)  D: $( - \infty , - 2 ] , R : ( - \infty , \infty )$ 
A)  D: $( - \infty , 0 ]$, R: $[ - 2 , \infty )$ 
B)  D: $( - \infty , \infty ) , \mathrm { R } : ( - \infty , - 2 ]$ 
C)  D: $[ 0 , \infty ) , \mathrm { R } : ( - \infty , - 2 ]$ 
D)  D: $( - \infty , - 2 ] , R : ( - \infty , \infty )$

Question 17

The variable s is proportional to t, and s = 50 when t = 150. Determine t when s = 75.

Accepted Answer

A)  3 
B)  300 
C)  225 
D)  215 
A)  3 
B)  300 
C)  225 
D)  215

Question 18

Determine if the function is even, odd, or neither.
-$$g ( x ) = \left| 5 x ^ { 3 } \right|$$

Accepted Answer

A)  Even 
B)  Odd 
C)  Neither 
A)  Even 
B)  Odd 
C)  Neither

Question 19

Find the domain and range for the indicated function.
-If $f ( x ) = \frac { x - 4 } { 9 }$ and $g ( x ) = 9 x + 4$, find $g ( f ( x ) )$

Accepted Answer

A)  $- \frac { 4 } { 9 }$ 
B)  $9 x + 32$ 
C)  $x$ 
D)  $x + 8$ 
A)  $- \frac { 4 } { 9 }$ 
B)  $9 x + 32$ 
C)  $x$ 
D)  $x + 8$

Question 20

Find the domain and range of the function.
-$$g ( z ) = \frac { - 5 } { \sqrt { z + 1 } }$$

Accepted Answer

A)  D: $( - \infty , - 1 )$, R: $( 0 , \infty )$ 
B)  D: $[ 1 , \infty ) , R : ( - \infty , \infty )$ 
C)  D: $[ 0 , \infty )$, R: $( - \infty , \infty )$ 
D)  D: $( - 1 , \infty ) , \mathrm { R } : ( - \infty , 0 )$ 
A)  D: $( - \infty , - 1 )$, R: $( 0 , \infty )$ 
B)  D: $[ 1 , \infty ) , R : ( - \infty , \infty )$ 
C)  D: $[ 0 , \infty )$, R: $( - \infty , \infty )$ 
D)  D: $( - 1 , \infty ) , \mathrm { R } : ( - \infty , 0 )$

Express the given function as a composite of functions f and g such that y = f(g(x)). - $y = ( 8 x - 19 ) ^ { 4 }$

Determine if the function is even, odd, or neither. - $f ( x ) = 3 x ^ { 2 } + 2$

Find the domain and range of the function. - $F ( t ) = \frac { 6 } { \sqrt { t } }$

Express the given function as a composite of functions f and g such that y = f(g(x)). - $y = \frac { 1 } { x ^ { 2 } - 7 }$

Find the domain and graph the function. -f(x) = 4x + 9

Determine if the function is even, odd, or neither. - $f ( x ) = \frac { 5 } { x + 9 }$

Find the domain and range for the indicated function. - $f ( x ) = \sqrt { x + 11 } , \quad g ( x ) = \sqrt { x - 11 }$ $\mathrm { f } - \mathrm { g }$

Graph the function. - $f ( x ) = \left\{ \begin{array} { l l } 4 x + 2 , & x < - 2 \\x , & - 2 \leq x \leq 3 \\3 x - 1 , & x > 3\end{array} \right.$ $Graph the function. - f ( x ) = \left\{ \begin{array} { l l } 4 x + 2 , & x < - 2 \\ x , & - 2 \leq x \leq 3 \\ 3 x - 1 , & x > 3 \end{array} \right.$

Express the given function as a composite of functions f and g such that y = f(g(x)). -Let $g ( x ) = x + 8$ . Find a function $y = f ( x )$ so that $( f \circ g ) ( x ) = 3 x + 24$

Express the given function as a composite of functions f and g such that y = f(g(x)). - $y = | 4 x + 10 |$

Provide an appropriate response. - $\text { Consider the function } y = \sqrt { 1 - \frac { 1 } { x } } . \text { Can } x \text { be greater than } 0 \text {, but less than } 1 \text { ? }$

Determine whether or not the graph is a graph of a function of x. -

Find the domain and graph the function. - $F ( t ) = \frac { | t - 1 | } { t - 1 }$ $Find the domain and graph the function. - F ( t ) = \frac { | t - 1 | } { t - 1 }$

Graph the function. - $f ( x ) = \left\{ \begin{array} { l l } - 2 - x , & x < 1 \\1 , & x \geq 1\end{array} \right.$ $Graph the function. - f ( x ) = \left\{ \begin{array} { l l } - 2 - x , & x < 1 \\ 1 , & x \geq 1 \end{array} \right.$

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 inches by 29 inches by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x.

Find the domain and range of the function. - $g ( z ) = - 2 - \sqrt { z }$

The variable s is proportional to t, and s = 50 when t = 150. Determine t when s = 75.

Determine if the function is even, odd, or neither. - $g ( x ) = \left| 5 x ^ { 3 } \right|$

Find the domain and range for the indicated function. -If $f ( x ) = \frac { x - 4 } { 9 }$ and $g ( x ) = 9 x + 4$ , find $g ( f ( x ) )$

Find the domain and range of the function. - $g ( z ) = \frac { - 5 } { \sqrt { z + 1 } }$

Limits and Derivatives

Differentiation

Applications of Derivatives

Integration

Applications of Definite Integrals

Integrals and Transcendental Functions

Techniques of Integration

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Infinite Sequences and Series

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Exam 1: Functions

Express the given function as a composite of functions f and g such that y = f(g(x)). - y=(8x−19)4y = ( 8 x - 19 ) ^ { 4 }y=(8x−19)4

Determine if the function is even, odd, or neither. - f(x)=3x2+2f ( x ) = 3 x ^ { 2 } + 2f(x)=3x2+2

Find the domain and range of the function. - F(t)=6tF ( t ) = \frac { 6 } { \sqrt { t } }F(t)=t​6​

Express the given function as a composite of functions f and g such that y = f(g(x)). - y=1x2−7y = \frac { 1 } { x ^ { 2 } - 7 }y=x2−71​

Find the domain and graph the function. -f(x) = 4x + 9

Determine if the function is even, odd, or neither. - f(x)=5x+9f ( x ) = \frac { 5 } { x + 9 }f(x)=x+95​

Find the domain and range for the indicated function. - f(x)=x+11,g(x)=x−11f ( x ) = \sqrt { x + 11 } , \quad g ( x ) = \sqrt { x - 11 }f(x)=x+11​,g(x)=x−11​ f−g\mathrm { f } - \mathrm { g }f−g

Graph the function. - f(x)={4x+2,x<−2x,−2≤x≤33x−1,x>3f ( x ) = \left\{ \begin{array} { l l } 4 x + 2 , & x < - 2 \\x , & - 2 \leq x \leq 3 \\3 x - 1 , & x > 3\end{array} \right.f(x)=⎩⎨⎧​4x+2,x,3x−1,​x<−2−2≤x≤3x>3​

Express the given function as a composite of functions f and g such that y = f(g(x)). -Let g(x)=x+8g ( x ) = x + 8g(x)=x+8 . Find a function y=f(x)y = f ( x )y=f(x) so that (f∘g)(x)=3x+24( f \circ g ) ( x ) = 3 x + 24(f∘g)(x)=3x+24

Express the given function as a composite of functions f and g such that y = f(g(x)). - y=∣4x+10∣y = | 4 x + 10 |y=∣4x+10∣

Determine whether or not the graph is a graph of a function of x. -

Find the domain and graph the function. - F(t)=∣t−1∣t−1F ( t ) = \frac { | t - 1 | } { t - 1 }F(t)=t−1∣t−1∣​

Graph the function. - f(x)={−2−x,x<11,x≥1f ( x ) = \left\{ \begin{array} { l l } - 2 - x , & x < 1 \\1 , & x \geq 1\end{array} \right.f(x)={−2−x,1,​x<1x≥1​

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 inches by 29 inches by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x.

Find the domain and range of the function. - g(z)=−2−zg ( z ) = - 2 - \sqrt { z }g(z)=−2−z​

The variable s is proportional to t, and s = 50 when t = 150. Determine t when s = 75.

Determine if the function is even, odd, or neither. - g(x)=∣5x3∣g ( x ) = \left| 5 x ^ { 3 } \right|g(x)=​5x3​

Find the domain and range for the indicated function. -If f(x)=x−49f ( x ) = \frac { x - 4 } { 9 }f(x)=9x−4​ and g(x)=9x+4g ( x ) = 9 x + 4g(x)=9x+4 , find g(f(x))g ( f ( x ) )g(f(x))

Find the domain and range of the function. - g(z)=−5z+1g ( z ) = \frac { - 5 } { \sqrt { z + 1 } }g(z)=z+1​−5​

Limits and Derivatives

Differentiation

Applications of Derivatives

Integration

Applications of Definite Integrals

Integrals and Transcendental Functions

Techniques of Integration

First-Order Differential Equations

Infinite Sequences and Series

Filters

Express the given function as a composite of functions f and g such that y = f(g(x)). - $y = ( 8 x - 19 ) ^ { 4 }$

Determine if the function is even, odd, or neither. - $f ( x ) = 3 x ^ { 2 } + 2$

Find the domain and range of the function. - $F ( t ) = \frac { 6 } { \sqrt { t } }$

Express the given function as a composite of functions f and g such that y = f(g(x)). - $y = \frac { 1 } { x ^ { 2 } - 7 }$

Determine if the function is even, odd, or neither. - $f ( x ) = \frac { 5 } { x + 9 }$

Find the domain and range for the indicated function. - $f ( x ) = \sqrt { x + 11 } , \quad g ( x ) = \sqrt { x - 11 }$ $\mathrm { f } - \mathrm { g }$

Express the given function as a composite of functions f and g such that y = f(g(x)). -Let $g ( x ) = x + 8$ . Find a function $y = f ( x )$ so that $( f \circ g ) ( x ) = 3 x + 24$

Express the given function as a composite of functions f and g such that y = f(g(x)). - $y = | 4 x + 10 |$

Find the domain and graph the function. - $F ( t ) = \frac { | t - 1 | } { t - 1 }$ $Find the domain and graph the function. - F ( t ) = \frac { | t - 1 | } { t - 1 }$

Graph the function. - $f ( x ) = \left\{ \begin{array} { l l } - 2 - x , & x < 1 \\1 , & x \geq 1\end{array} \right.$ $Graph the function. - f ( x ) = \left\{ \begin{array} { l l } - 2 - x , & x < 1 \\ 1 , & x \geq 1 \end{array} \right.$

Find the domain and range of the function. - $g ( z ) = - 2 - \sqrt { z }$

Determine if the function is even, odd, or neither. - $g ( x ) = \left| 5 x ^ { 3 } \right|$

Find the domain and range for the indicated function. -If $f ( x ) = \frac { x - 4 } { 9 }$ and $g ( x ) = 9 x + 4$ , find $g ( f ( x ) )$

Find the domain and range of the function. - $g ( z ) = \frac { - 5 } { \sqrt { z + 1 } }$