Question 1

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing.
-$y=-|x|$

Accepted Answer

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

B

Question 2

Express the given function as a composite of functions f and g such that y = f(g(x)).
-$y = \frac { 1 } { x ^ { 2 } } + 8$

Accepted Answer

A)  $f ( x ) = x + 8 , g ( x ) = \frac { 1 } { x ^ { 2 } }$ 
B)  $f ( x ) = x , g ( x ) = \frac { 1 } { x } + 8$ 
C)  $f ( x ) = \frac { 1 } { x } , g ( x ) = \frac { 1 } { x } + 8$ 
D)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = 8$ 
A)  $f ( x ) = x + 8 , g ( x ) = \frac { 1 } { x ^ { 2 } }$ 
B)  $f ( x ) = x , g ( x ) = \frac { 1 } { x } + 8$ 
C)  $f ( x ) = \frac { 1 } { x } , g ( x ) = \frac { 1 } { x } + 8$ 
D)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = 8$ A

Question 3

Find the domain and range of the function.
-$$f ( x ) = \frac { 7 } { 10 + \sqrt { x } }$$

Accepted Answer

A)  D: $( - \infty , \infty ) , R : \left( 0 , \frac { 7 } { 10 } \right]$ 
B)  D: $[ 0 , \infty ) , \mathrm { R } : \left[ 0 , \frac { 7 } { 10 } \right]$ 
C)  D: $[ 0 , \infty )$, R: $( - \infty , \infty )$ 
D)  D: $( - \infty , 0 ] , \mathrm { R } : ( - \infty , 0 ]$ 
A)  D: $( - \infty , \infty ) , R : \left( 0 , \frac { 7 } { 10 } \right]$ 
B)  D: $[ 0 , \infty ) , \mathrm { R } : \left[ 0 , \frac { 7 } { 10 } \right]$ 
C)  D: $[ 0 , \infty )$, R: $( - \infty , \infty )$ 
D)  D: $( - \infty , 0 ] , \mathrm { R } : ( - \infty , 0 ]$ B

Question 4

Provide an appropriate response.
-What is the domain of the function $y = \sqrt { 1 - \frac { 1 } { x } }$ ?

Accepted Answer

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

Question 5

Provide an appropriate response.
-For what values of $x$ is $\lfloor x \rfloor = 3$ ?

Accepted Answer

A)  $2 < x \leq 3$ 
B)  $2 \leq x < 3$ 
C)  $3 < x \leq 4$ 
D)  $3 \leq x < 4$ 
A)  $2 < x \leq 3$ 
B)  $2 \leq x < 3$ 
C)  $3 < x \leq 4$ 
D)  $3 \leq x < 4$

Question 6

Find the domain and range of the function.
-$$f ( x ) = - 2 + \sqrt { x }$$

Accepted Answer

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

Question 7

Provide an appropriate response.
-$\text { Graph the function } f ( x ) = \lfloor x \rfloor \text {. }$

Accepted Answer

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

Question 8

Express the given function as a composite of functions f and g such that y = f(g(x)).
-Let $f ( x ) = \sqrt { x - 5 }$. Find a function $y = g ( x )$ so that $( f \circ g ) ( x ) = \sqrt { x ^ { 2 } - 5 }$.

Accepted Answer

A)  $g ( x ) = x ^ { 2 } + 5$ 
B)  $g ( x ) = 2 x$ 
C)  $g ( x ) = x ^ { 2 }$ 
D)  $g ( x ) = x ^ { 2 } - 5$ 
A)  $g ( x ) = x ^ { 2 } + 5$ 
B)  $g ( x ) = 2 x$ 
C)  $g ( x ) = x ^ { 2 }$ 
D)  $g ( x ) = x ^ { 2 } - 5$

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

A)  $y = - x ^ { 2 } + 6$ 
B)  $y = - ( x - 6 ) ^ { 2 }$ 
C)  $y = - ( x + 6 ) ^ { 2 }$ 
D)  $y = - x ^ { 2 } - 6$ 
A)  $y = - x ^ { 2 } + 6$ 
B)  $y = - ( x - 6 ) ^ { 2 }$ 
C)  $y = - ( x + 6 ) ^ { 2 }$ 
D)  $y = - x ^ { 2 } - 6$

Question 11

Find a formula for the function graphed.
-

Accepted Answer

A)  $f ( x ) = \left\{ \begin{array} { l l } 4 , & x \leq 0 \ - 4 , & x > 0 \end{array} \right.$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } 4 x , & x \leq 0 \ - 4 x , & x > 0 \end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } 4 , & x  0 \end{array} \right.$ 
A)  $f ( x ) = \left\{ \begin{array} { l l } 4 , & x \leq 0 \ - 4 , & x > 0 \end{array} \right.$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } 4 x , & x \leq 0 \ - 4 x , & x > 0 \end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } 4 , & x  0 \end{array} \right.$

Question 12

Graph the function. Determine the symmetry, if any, of the function.
-$y = \sqrt { - x }$

Accepted Answer

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

Question 13

Find the domain and range for the indicated function.
-$f ( x ) = 8 , \quad g ( x ) = 8 + \sqrt { x }$  ; $\mathrm { f } / \mathrm { g }$

Accepted Answer

A)  D: $x \geq - 8$
R: $y \geq 0$ 
B)  D: $x \geq 0$
R: $y \leq 8$ 
C)  D: $x \geq 0$
R: $y \leq 1$ 
D)  D: $x \geq 0$
R: $y \geq 1$ 
A)  D: $x \geq - 8$
R: $y \geq 0$ 
B)  D: $x \geq 0$
R: $y \leq 8$ 
C)  D: $x \geq 0$
R: $y \leq 1$ 
D)  D: $x \geq 0$
R: $y \geq 1$

Question 14

Provide an appropriate response.
-$\text { Graph the equation } y ^ { 2 } = x \text { and decide whether or not the graph represents a function of } x \text {. }$

Accepted Answer

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

Question 15

Find the domain and graph the function.
-$g(x)=-7+2 x-x^{2}$

Accepted Answer

A)  D: $( - \infty , \infty )$
  
B)  D: $( - \infty , \infty )$
  
C)  D: $( - \infty , \infty )$
  
D)  D: $( - \infty , - 6 ]$
  
A)  D: $( - \infty , \infty )$
  
B)  D: $( - \infty , \infty )$
  
C)  D: $( - \infty , \infty )$
  
D)  D: $( - \infty , - 6 ]$

Question 16

Determine if the function is even, odd, or neither.
-$f ( x ) = 4 x ^ { 4 } - 6 x - 5$

Accepted Answer

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

Question 17

Boyle's Law says that volume $\mathrm { V }$ of a gas at constant temperature increases whenever the pressure $\mathrm { P }$ decreases, so that $\mathrm { V }$ and $\mathrm { P }$ are inversely proportional. If $\mathrm { P } = 14.1 \mathrm { lbs } / \mathrm { in } ^ { 2 }$ when $\mathrm { V } = 900$ in ${ } ^ { 3 }$, then what is $\mathrm { V }$ when $\mathrm { P } = 21 \mathrm { lbs } /$ in $^ { 2 }$ ?

Accepted Answer

A)  $\frac { 1000 } { 329 }$ in 3 
B)  $\frac { 329 } { 1000 }$ in $^ { 3 }$ 
C)  $\frac { 4230 } { 7 }$ in 3 
D)  $\frac { 63000 } { 47 } \mathrm { in } ^ { 3 }$ 
A)  $\frac { 1000 } { 329 }$ in 3 
B)  $\frac { 329 } { 1000 }$ in $^ { 3 }$ 
C)  $\frac { 4230 } { 7 }$ in 3 
D)  $\frac { 63000 } { 47 } \mathrm { in } ^ { 3 }$

Question 18

Determine if the function is even, odd, or neither.
-$$f ( x ) = \frac { 5 } { x ^ { 2 } + 4 }$$

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.
-$f ( x ) = \sqrt { x + 10 } , \quad g ( x ) = \sqrt { x - 10 } ; \quad f \cdot g$

Accepted Answer

A) D: $x > 10$ R: $y \geq 0$ B) D: $x \geq 10$ R: $y > 0$ C) D: $x \geq 10$ R: $- \infty < y < \infty$ D) D: $x \geq 10$ R: $y \geq 0$ A) D: $x > 10$ R: $y \geq 0$ B) D: $x \geq 10$ R: $y > 0$ C) D: $x \geq 10$ R: $- \infty < y < \infty$ D) D: $x \geq 10$ R: $y \geq 0$

Question 20

Find the domain and range of the function.
-$$F ( t ) = t ^ { 2 } - 3$$

Accepted Answer

A)  D: $( - \infty , \infty )$, R: $[ - 3 , \infty )$ 
B)  D: $( - \infty , \infty )$, R: $( - \infty , \infty )$ 
C)  D: $[ 0 , \infty )$, R: $( - \infty , - 3 ]$ 
D)  D: $[ - 9 , \infty )$, R: $[ - 3 , \infty )$ 
A)  D: $( - \infty , \infty )$, R: $[ - 3 , \infty )$ 
B)  D: $( - \infty , \infty )$, R: $( - \infty , \infty )$ 
C)  D: $[ 0 , \infty )$, R: $( - \infty , - 3 ]$ 
D)  D: $[ - 9 , \infty )$, R: $[ - 3 , \infty )$

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - $y=-|x|$

Express the given function as a composite of functions f and g such that y = f(g(x)). - $y = \frac { 1 } { x ^ { 2 } } + 8$

Find the domain and range of the function. - $f ( x ) = \frac { 7 } { 10 + \sqrt { x } }$

Provide an appropriate response. -What is the domain of the function $y = \sqrt { 1 - \frac { 1 } { x } }$ ?

Provide an appropriate response. -For what values of $x$ is $\lfloor x \rfloor = 3$ ?

Find the domain and range of the function. - $f ( x ) = - 2 + \sqrt { x }$

Provide an appropriate response. - $\text { Graph the function } f ( x ) = \lfloor x \rfloor \text {. }$ $Provide an appropriate response. - \text { Graph the function } f ( x ) = \lfloor x \rfloor \text {. }$

Express the given function as a composite of functions f and g such that y = f(g(x)). -Let $f ( x ) = \sqrt { x - 5 }$ . Find a function $y = g ( x )$ so that $( f \circ g ) ( x ) = \sqrt { x ^ { 2 } - 5 }$ .

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

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

Find a formula for the function graphed. -

Graph the function. Determine the symmetry, if any, of the function. - $y = \sqrt { - x }$ $Graph the function. Determine the symmetry, if any, of the function. - y = \sqrt { - x }$

Find the domain and range for the indicated function. - $f ( x ) = 8 , \quad g ( x ) = 8 + \sqrt { x }$ ; $\mathrm { f } / \mathrm { g }$

Find the domain and graph the function. - $g(x)=-7+2 x-x^{2}$ $Find the domain and graph the function. - g(x)=-7+2 x-x^{2}$

Determine if the function is even, odd, or neither. - $f ( x ) = 4 x ^ { 4 } - 6 x - 5$

Determine if the function is even, odd, or neither. - $f ( x ) = \frac { 5 } { x ^ { 2 } + 4 }$

Find the domain and range for the indicated function. - $f ( x ) = \sqrt { x + 10 } , \quad g ( x ) = \sqrt { x - 10 } ; \quad f \cdot g$

Find the domain and range of the function. - $F ( t ) = t ^ { 2 } - 3$

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Exam 1: Functions

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y=−∣x∣y=-|x|y=−∣x∣

Express the given function as a composite of functions f and g such that y = f(g(x)). - y=1x2+8y = \frac { 1 } { x ^ { 2 } } + 8y=x21​+8

Find the domain and range of the function. - f(x)=710+xf ( x ) = \frac { 7 } { 10 + \sqrt { x } }f(x)=10+x​7​

Provide an appropriate response. -What is the domain of the function y=1−1xy = \sqrt { 1 - \frac { 1 } { x } }y=1−x1​​ ?

Provide an appropriate response. -For what values of xxx is ⌊x⌋=3\lfloor x \rfloor = 3⌊x⌋=3 ?

Find the domain and range of the function. - f(x)=−2+xf ( x ) = - 2 + \sqrt { x }f(x)=−2+x​

Provide an appropriate response. - Graph the function f(x)=⌊x⌋. \text { Graph the function } f ( x ) = \lfloor x \rfloor \text {. } Graph the function f(x)=⌊x⌋.

Express the given function as a composite of functions f and g such that y = f(g(x)). -Let f(x)=x−5f ( x ) = \sqrt { x - 5 }f(x)=x−5​ . Find a function y=g(x)y = g ( x )y=g(x) so that (f∘g)(x)=x2−5( f \circ g ) ( x ) = \sqrt { x ^ { 2 } - 5 }(f∘g)(x)=x2−5​ .

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y=−x2/5y=-x^{2 / 5}y=−x2/5