Question 1

The accompanying figure shows the graph of y = x2 shifted to a new position. Write the equation for the new graph.

Accepted Answer

A)  $y = ( x + 1 ) ^ { 2 } + 2$ 
B)  $y = ( x + 1 ) ^ { 2 } - 2$ 
C)  $y = ( x - 1 ) ^ { 2 } + 2$ 
D)  $y = ( x - 2 ) ^ { 2 } + 1$ 
A)  $y = ( x + 1 ) ^ { 2 } + 2$ 
B)  $y = ( x + 1 ) ^ { 2 } - 2$ 
C)  $y = ( x - 1 ) ^ { 2 } + 2$ 
D)  $y = ( x - 2 ) ^ { 2 } + 1$

Question 2

Find the domain and range for the indicated function.
-If $f ( x ) = \sqrt { x + 5 }$ and $g ( x ) = 8 x - 9$, find $f ( g ( x ) )$.

Accepted Answer

A)  $8 \sqrt { x - 4 }$ 
B)  $8 \sqrt { x + 5 } - 9$ 
C)  $2 \sqrt { 2 x + 1 }$ 
D)  $2 \sqrt { 2 x - 1 }$ 
A)  $8 \sqrt { x - 4 }$ 
B)  $8 \sqrt { x + 5 } - 9$ 
C)  $2 \sqrt { 2 x + 1 }$ 
D)  $2 \sqrt { 2 x - 1 }$

Question 3

Provide an appropriate response.
-Graph the functions $f ( x ) = \frac { x } { 2 }$ and $g ( x ) = 3 + \frac { 8 } { x }$ together to identify the values of $x$ for which $\frac { x } { 2 } > 3 + \frac { 8 } { x }$. Confirm your findings algebraically.

Accepted Answer

A)  $( - 2,0 ) \cup ( 8 , \infty )$ 
B)  $( 8 , \infty )$ 
C)  $( - \infty , - 2 ) \cup ( 0,8 )$ 
D)  $( - 2,8 )$ 
A)  $( - 2,0 ) \cup ( 8 , \infty )$ 
B)  $( 8 , \infty )$ 
C)  $( - \infty , - 2 ) \cup ( 0,8 )$ 
D)  $( - 2,8 )$

Question 4

Find the domain and range for the indicated function.
-If $f ( x ) = \sqrt { x } , g ( x ) = \frac { x } { 5 }$, and $h ( x ) = 5 x + 10$, find $h ( g ( f ( x ) ) )$

Accepted Answer

A)  $\sqrt { x + 2 }$ 
B)  $5 \sqrt { x } + 10$ 
C)  $\sqrt { x } + 10$ 
D)  $\sqrt { x } + 2$ 
A)  $\sqrt { x + 2 }$ 
B)  $5 \sqrt { x } + 10$ 
C)  $\sqrt { x } + 10$ 
D)  $\sqrt { x } + 2$

Question 5

Find the domain and range for the indicated function.
-If $f ( x ) = - 2 x - 9$ and $g ( x ) = - 4 x ^ { 2 } - 7 x + 1$, find $g ( f ( - 2 ) )$.

Accepted Answer

A)  $- 64$ 
B)  $- 7$ 
C)  $- 55$ 
D)  56 
A)  $- 64$ 
B)  $- 7$ 
C)  $- 55$ 
D)  56

Question 6

Provide an appropriate response.
-For what values of $x$ is $\lceil x \rceil = - 1$ ?

Accepted Answer

A)  $- 2 \leq x < - 1$ 
B)  $- 2 < x \leq - 1$ 
C)  $- 1 \leq x < 0$ 
D)  $- 1 < x \leq 0$ 
A)  $- 2 \leq x < - 1$ 
B)  $- 2 < x \leq - 1$ 
C)  $- 1 \leq x < 0$ 
D)  $- 1 < x \leq 0$

Question 7

Graph the function. Determine the symmetry, if any, of the function.
-$y=-x^{2 / 3}$

Accepted Answer

A)  No symmetry
  
B)  Symmetric about the $y$-axis
  
C)  Symmetric about the $y$-axis
  
D)  No symmetry
  
A)  No symmetry
  
B)  Symmetric about the $y$-axis
  
C)  Symmetric about the $y$-axis
  
D)  No symmetry

Question 8

Graph the function. Determine the symmetry, if any, of the function.
-$y = - \frac { 1 } { x ^ { 2 } }$

Accepted Answer

A)  Symmetric about the $y$-axis
  
B)  Symmetric about the $y$-axis
  
C)  No symmetry
  
D)  Symmetric about the $y$-axis
  
A)  Symmetric about the $y$-axis
  
B)  Symmetric about the $y$-axis
  
C)  No symmetry
  
D)  Symmetric about the $y$-axis

Question 9

Graph the function.
-$$g ( x ) = \left\{ \begin{array} { l l } 
2 & x \leq 0 \
x + 1 , & x > 0
\end{array} \right.$$

Accepted Answer

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

Question 10

Find the domain and range for the indicated function.
-If $f ( x ) = \sqrt { x } , g ( x ) = \frac { x } { 3 }$, and $h ( x ) = 3 x + 9$, find $f ( g ( h ( x ) ) )$

Accepted Answer

A)  $\sqrt { x + 9 }$ 
B)  $\sqrt { x + 3 }$ 
C)  $\sqrt { x } + 3$ 
D)  $3 \sqrt { x } + 9$ 
A)  $\sqrt { x + 9 }$ 
B)  $\sqrt { x + 3 }$ 
C)  $\sqrt { x } + 3$ 
D)  $3 \sqrt { x } + 9$

Question 11

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 12

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing.
-$y=(-x)^{5 / 2}$

Accepted Answer

A)  Decreasing $- \infty < x < \infty$
  
B)  Decreasing $- \infty < x \leq 0$
 Increasing $0 \leq x < \infty$
  
C)  Decreasing $- \infty < x \leq 0$
  
D)  Increasing $0 \leq x < \infty$
  
A)  Decreasing $- \infty < x < \infty$
  
B)  Decreasing $- \infty < x \leq 0$
 Increasing $0 \leq x < \infty$
  
C)  Decreasing $- \infty < x \leq 0$
  
D)  Increasing $0 \leq x < \infty$

Question 13

Find the domain and range for the indicated function.
-If f(x) = 3x + 8 and g(x) = 3x - 1, find f(g(x)).

Accepted Answer

A)  9x + 5 
B)  9x + 7 
C)  9x + 23 
D)  9x + 11 
A)  9x + 5 
B)  9x + 7 
C)  9x + 23 
D)  9x + 11

Question 14

Determine if the function is even, odd, or neither.
-$$g ( x ) = \frac { - 5 x } { x ^ { 2 } + 3 }$$

Accepted Answer

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

Question 15

Find the domain and range for the indicated function.
-If $f ( x ) = 4 x ^ { 2 } + 6 x + 8$ and $g ( x ) = 6 x - 7$, find $g ( f ( x ) )$

Accepted Answer

A)  $4 x ^ { 2 } + 36 x + 41$ 
B)  $24 x ^ { 2 } + 36 x + 55$ 
C)  $4 x ^ { 2 } + 6 x + 1$ 
D)  $24 x ^ { 2 } + 36 x + 41$ 
A)  $4 x ^ { 2 } + 36 x + 41$ 
B)  $24 x ^ { 2 } + 36 x + 55$ 
C)  $4 x ^ { 2 } + 6 x + 1$ 
D)  $24 x ^ { 2 } + 36 x + 41$

Question 16

The accompanying figure shows the graph of y = -x2 shifted to a new position. Write the equation for the new graph.

Accepted Answer

A)  $y = - x ^ { 2 } + 3$ 
B)  $y = - x ^ { 2 } - 3$ 
C)  $y = - ( x + 3 ) ^ { 2 }$ 
D)  $y = - ( x - 3 ) ^ { 2 }$ 
A)  $y = - x ^ { 2 } + 3$ 
B)  $y = - x ^ { 2 } - 3$ 
C)  $y = - ( x + 3 ) ^ { 2 }$ 
D)  $y = - ( x - 3 ) ^ { 2 }$

Question 17

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

Accepted Answer

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

Question 18

Determine if the function is even, odd, or neither.
-$$h ( t ) = \sqrt { t ^ { 2 } - 8 }$$

Accepted Answer

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

Question 19

Graph the function.
-$$\mathrm { F } ( \mathrm { x } ) = \left\{ \begin{array} { l l } 
4 - \mathrm { x } , & \mathrm { x } \leq 2 \
1 - 3 \mathrm { x } , & \mathrm { x } > 2 \

\end{array} \right.$$

Accepted Answer

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

Question 20

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

Accepted Answer

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

The accompanying figure shows the graph of y = x2 shifted to a new position. Write the equation for the new graph.

Find the domain and range for the indicated function. -If $f ( x ) = \sqrt { x + 5 }$ and $g ( x ) = 8 x - 9$ , find $f ( g ( x ) )$ .

Provide an appropriate response. -Graph the functions $f ( x ) = \frac { x } { 2 }$ and $g ( x ) = 3 + \frac { 8 } { x }$ together to identify the values of $x$ for which $\frac { x } { 2 } > 3 + \frac { 8 } { x }$ . Confirm your findings algebraically.

Find the domain and range for the indicated function. -If $f ( x ) = \sqrt { x } , g ( x ) = \frac { x } { 5 }$ , and $h ( x ) = 5 x + 10$ , find $h ( g ( f ( x ) ) )$

Find the domain and range for the indicated function. -If $f ( x ) = - 2 x - 9$ and $g ( x ) = - 4 x ^ { 2 } - 7 x + 1$ , find $g ( f ( - 2 ) )$ .

Provide an appropriate response. -For what values of $x$ is $\lceil x \rceil = - 1$ ?

Graph the function. Determine the symmetry, if any, of the function. - $y=-x^{2 / 3}$ $Graph the function. Determine the symmetry, if any, of the function. - y=-x^{2 / 3}$

Graph the function. Determine the symmetry, if any, of the function. - $y = - \frac { 1 } { x ^ { 2 } }$ $Graph the function. Determine the symmetry, if any, of the function. - y = - \frac { 1 } { x ^ { 2 } }$

Graph the function. - $g ( x ) = \left\{ \begin{array} { l l } 2 & x \leq 0 \\x + 1 , & x > 0\end{array} \right.$ $Graph the function. - g ( x ) = \left\{ \begin{array} { l l } 2 & x \leq 0 \\ x + 1 , & x > 0 \end{array} \right.$

Find the domain and range for the indicated function. -If $f ( x ) = \sqrt { x } , g ( x ) = \frac { x } { 3 }$ , and $h ( x ) = 3 x + 9$ , find $f ( g ( h ( x ) ) )$

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

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - $y=(-x)^{5 / 2}$ $Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y=(-x)^{5 / 2}$

Find the domain and range for the indicated function. -If f(x) = 3x + 8 and g(x) = 3x - 1, find f(g(x)).

Determine if the function is even, odd, or neither. - $g ( x ) = \frac { - 5 x } { x ^ { 2 } + 3 }$

Find the domain and range for the indicated function. -If $f ( x ) = 4 x ^ { 2 } + 6 x + 8$ and $g ( x ) = 6 x - 7$ , find $g ( f ( x ) )$

The accompanying figure shows the graph of y = -x² shifted to a new position. Write the equation for the new graph.

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

Determine if the function is even, odd, or neither. - $h ( t ) = \sqrt { t ^ { 2 } - 8 }$

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

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Exam 1: Functions

The accompanying figure shows the graph of y = x2 shifted to a new position. Write the equation for the new graph.

Find the domain and range for the indicated function. -If f(x)=x+5f ( x ) = \sqrt { x + 5 }f(x)=x+5​ and g(x)=8x−9g ( x ) = 8 x - 9g(x)=8x−9 , find f(g(x))f ( g ( x ) )f(g(x)) .

Find the domain and range for the indicated function. -If f(x)=x,g(x)=x5f ( x ) = \sqrt { x } , g ( x ) = \frac { x } { 5 }f(x)=x​,g(x)=5x​ , and h(x)=5x+10h ( x ) = 5 x + 10h(x)=5x+10 , find h(g(f(x)))h ( g ( f ( x ) ) )h(g(f(x)))

Find the domain and range for the indicated function. -If f(x)=−2x−9f ( x ) = - 2 x - 9f(x)=−2x−9 and g(x)=−4x2−7x+1g ( x ) = - 4 x ^ { 2 } - 7 x + 1g(x)=−4x2−7x+1 , find g(f(−2))g ( f ( - 2 ) )g(f(−2)) .

Provide an appropriate response. -For what values of xxx is ⌈x⌉=−1\lceil x \rceil = - 1⌈x⌉=−1 ?

Graph the function. Determine the symmetry, if any, of the function. - y=−x2/3y=-x^{2 / 3}y=−x2/3

Graph the function. Determine the symmetry, if any, of the function. - y=−1x2y = - \frac { 1 } { x ^ { 2 } }y=−x21​

Graph the function. - g(x)={2x≤0x+1,x>0g ( x ) = \left\{ \begin{array} { l l } 2 & x \leq 0 \\x + 1 , & x > 0\end{array} \right.g(x)={2x+1,​x≤0x>0​

Find the domain and range for the indicated function. -If f(x)=x,g(x)=x3f ( x ) = \sqrt { x } , g ( x ) = \frac { x } { 3 }f(x)=x​,g(x)=3x​ , and h(x)=3x+9h ( x ) = 3 x + 9h(x)=3x+9 , find f(g(h(x)))f ( g ( h ( x ) ) )f(g(h(x)))

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

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y=(−x)5/2y=(-x)^{5 / 2}y=(−x)5/2

Find the domain and range for the indicated function. -If f(x) = 3x + 8 and g(x) = 3x - 1, find f(g(x)).

Determine if the function is even, odd, or neither. - g(x)=−5xx2+3g ( x ) = \frac { - 5 x } { x ^ { 2 } + 3 }g(x)=x2+3−5x​

Find the domain and range for the indicated function. -If f(x)=4x2+6x+8f ( x ) = 4 x ^ { 2 } + 6 x + 8f(x)=4x2+6x+8 and g(x)=6x−7g ( x ) = 6 x - 7g(x)=6x−7 , find g(f(x))g ( f ( x ) )g(f(x))

The accompanying figure shows the graph of y = -x2 shifted to a new position. Write the equation for the new graph.

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

Determine if the function is even, odd, or neither. - h(t)=t2−8h ( t ) = \sqrt { t ^ { 2 } - 8 }h(t)=t2−8​

Graph the function. - F(x)={4−x,x≤21−3x,x>2\mathrm { F } ( \mathrm { x } ) = \left\{ \begin{array} { l l } 4 - \mathrm { x } , & \mathrm { x } \leq 2 \\1 - 3 \mathrm { x } , & \mathrm { x } > 2 \\\end{array} \right.F(x)={4−x,1−3x,​x≤2x>2​

Graph the function. - g(x)={1x−2,x<2x,x≥2g ( x ) = \left\{ \begin{array} { l l } \frac { 1 } { x - 2 } , & x < 2 \\x , & x \geq 2\end{array} \right.g(x)={x−21​,x,​x<2x≥2​

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

Find the domain and range for the indicated function. -If $f ( x ) = \sqrt { x + 5 }$ and $g ( x ) = 8 x - 9$ , find $f ( g ( x ) )$ .

Find the domain and range for the indicated function. -If $f ( x ) = \sqrt { x } , g ( x ) = \frac { x } { 5 }$ , and $h ( x ) = 5 x + 10$ , find $h ( g ( f ( x ) ) )$

Find the domain and range for the indicated function. -If $f ( x ) = - 2 x - 9$ and $g ( x ) = - 4 x ^ { 2 } - 7 x + 1$ , find $g ( f ( - 2 ) )$ .

Provide an appropriate response. -For what values of $x$ is $\lceil x \rceil = - 1$ ?

Graph the function. Determine the symmetry, if any, of the function. - $y=-x^{2 / 3}$ $Graph the function. Determine the symmetry, if any, of the function. - y=-x^{2 / 3}$

Graph the function. Determine the symmetry, if any, of the function. - $y = - \frac { 1 } { x ^ { 2 } }$ $Graph the function. Determine the symmetry, if any, of the function. - y = - \frac { 1 } { x ^ { 2 } }$

Graph the function. - $g ( x ) = \left\{ \begin{array} { l l } 2 & x \leq 0 \\x + 1 , & x > 0\end{array} \right.$ $Graph the function. - g ( x ) = \left\{ \begin{array} { l l } 2 & x \leq 0 \\ x + 1 , & x > 0 \end{array} \right.$

Find the domain and range for the indicated function. -If $f ( x ) = \sqrt { x } , g ( x ) = \frac { x } { 3 }$ , and $h ( x ) = 3 x + 9$ , find $f ( g ( h ( x ) ) )$

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - $y=(-x)^{5 / 2}$ $Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y=(-x)^{5 / 2}$

Determine if the function is even, odd, or neither. - $g ( x ) = \frac { - 5 x } { x ^ { 2 } + 3 }$

Find the domain and range for the indicated function. -If $f ( x ) = 4 x ^ { 2 } + 6 x + 8$ and $g ( x ) = 6 x - 7$ , find $g ( f ( x ) )$

The accompanying figure shows the graph of y = -x² shifted to a new position. Write the equation for the new graph.

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

Determine if the function is even, odd, or neither. - $h ( t ) = \sqrt { t ^ { 2 } - 8 }$

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