Question 1

Give the domain and range of the relation.
-

Accepted Answer

A)  domain: $( - \infty , - 3 ) \cup ( - 3 , \infty )$; range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  domain: $( - \infty , 0 ] \cup [ 0 , \infty )$; range: $( - \infty , - 3 ] \cup [ - 3 , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
D)  domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; range: $( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
A)  domain: $( - \infty , - 3 ) \cup ( - 3 , \infty )$; range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  domain: $( - \infty , 0 ] \cup [ 0 , \infty )$; range: $( - \infty , - 3 ] \cup [ - 3 , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
D)  domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; range: $( - \infty , - 3 ) \cup ( - 3 , \infty )$

Question 2

For the pair of functions, find the indicated sum, difference, product, or quotient.
-$$f ( x ) = \sqrt { 6 x - 9 } , g ( x ) = \frac { 1 } { x }$$
Find $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } )$

Accepted Answer

A)  $\frac { \sqrt { 6 x - 9 } } { x }$ 
B)  $\frac { x } { \sqrt { 6 x - 9 } }$ 
C)  $x \sqrt { 6 x - 9 }$ 
D)  $\frac { 1 } { x \sqrt { 6 x - 9 } }$ 
A)  $\frac { \sqrt { 6 x - 9 } } { x }$ 
B)  $\frac { x } { \sqrt { 6 x - 9 } }$ 
C)  $x \sqrt { 6 x - 9 }$ 
D)  $\frac { 1 } { x \sqrt { 6 x - 9 } }$

Question 3

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph.
-$$x ^ { 2 } + y ^ { 2 } - 8 x + 12 y - 29 = 0$$

Accepted Answer

A)  no; the graph is the point $( - 4,6 )$ 
B)  no; the graph is nonexistent 
C)  yes 
D)  no; the graph is the point $( 4 , - 6 )$ 
A)  no; the graph is the point $( - 4,6 )$ 
B)  no; the graph is nonexistent 
C)  yes 
D)  no; the graph is the point $( 4 , - 6 )$

Question 4

Give a rule for the piecewise-defined function. Then give the domain and range.
-

Accepted Answer

A)  $f ( x ) = \left\{ \begin{array} { l l } x - 3 & \text { if } x \neq 3 \ - 2 & \text { if } x = 3 \end{array} ; \right.$ Domain: $( \infty , \infty )$, Range: $( \infty , 3 ] \cup [ 3 , \infty )$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } 2 x - 3 & \text { if } x \neq 3 \ - 3 & \text { if } x = 3 \end{array} ; \right.$ Domain: $( \infty , 3 ] \cup [ 3 , \infty )$, Range: $( \infty , \infty )$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } 2 x - 3 & \text { if } x \neq 3 \ - 2 & \text { if } x = 3 \end{array} ; \right.$ Domain: $( \infty , \infty )$, Range: $( \infty , 3 ) \cup ( 3 , \infty )$ 
D)  $f ( x ) = \left\{ \begin{array} { l } 2 x - 3 \text { if } x < 3 \ 2 x + 3 \text { if } x \geq 3 \end{array} ; \right.$ Domain: $( \infty , 3 ) \cup ( 3 , \infty )$, Range: $( \infty , \infty )$ 
A)  $f ( x ) = \left\{ \begin{array} { l l } x - 3 & \text { if } x \neq 3 \ - 2 & \text { if } x = 3 \end{array} ; \right.$ Domain: $( \infty , \infty )$, Range: $( \infty , 3 ] \cup [ 3 , \infty )$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } 2 x - 3 & \text { if } x \neq 3 \ - 3 & \text { if } x = 3 \end{array} ; \right.$ Domain: $( \infty , 3 ] \cup [ 3 , \infty )$, Range: $( \infty , \infty )$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } 2 x - 3 & \text { if } x \neq 3 \ - 2 & \text { if } x = 3 \end{array} ; \right.$ Domain: $( \infty , \infty )$, Range: $( \infty , 3 ) \cup ( 3 , \infty )$ 
D)  $f ( x ) = \left\{ \begin{array} { l } 2 x - 3 \text { if } x < 3 \ 2 x + 3 \text { if } x \geq 3 \end{array} ; \right.$ Domain: $( \infty , 3 ) \cup ( 3 , \infty )$, Range: $( \infty , \infty )$

Question 5

Select the equation that describes the graph shown.

Accepted Answer

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

Question 6

Graph the circle.
-$(x-2)^{2}+(y-4)^{2}=9$

Accepted Answer

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

Question 7

Match the description with the correct symbolic expression.
-a linear function whose graph has a slope of 8

Accepted Answer

A)  $f ( x ) = - 8 x + 8$ 
B)  $y = 8 x + 7$ 
C)  $8 x - 6 y = 7$ 
D)  $x = 8$ 
A)  $f ( x ) = - 8 x + 8$ 
B)  $y = 8 x + 7$ 
C)  $8 x - 6 y = 7$ 
D)  $x = 8$

Question 8

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-midpoint (c, y), endpoint (m, q)

Accepted Answer

A)  $\left( \frac { \mathrm { c } + \mathrm { m } } { 2 } , \frac { \mathrm { y } + \mathrm { q } } { 2 } \right)$ 
B)  $( 2 m - c , 2 q - y )$ 
C)  $( c - m , y - q )$ 
D)  $( 2 c - m , 2 y - q )$ 
A)  $\left( \frac { \mathrm { c } + \mathrm { m } } { 2 } , \frac { \mathrm { y } + \mathrm { q } } { 2 } \right)$ 
B)  $( 2 m - c , 2 q - y )$ 
C)  $( c - m , y - q )$ 
D)  $( 2 c - m , 2 y - q )$

Question 9

Graph the line described.
-$$\text { through } ( 0,4 ) ; \mathrm { m } = - \frac { 1 } { 6 }$$

Accepted Answer

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

Question 10

Describe the transformations and give the equation for the graph.
-

Accepted Answer

A)  It is the graph of $f ( x ) = \sqrt { x }$ translated 4 units to the right, shrunken vertically by a factor of $\frac { 1 } { 2 }$ and translated 3 units up. The equation is $y = \frac { 1 } { 2 } \sqrt { x + 4 } + 3$ 
B)  It is the graph of $\mathrm { f } ( \mathrm { x } ) = \sqrt { \mathrm { x } }$ translated 4 units to the right, stretched vertically by a factor of 2 and translated 3 units up. The equation is $y = 2 \sqrt { x - 4 } + 3$ 
C)  It is the graph of $f ( x ) = \sqrt { x }$ translated 4 units to the right, stretched vertically by a factor of 2 and translated 3 units up. The equation is $y = 2 \sqrt { x + 4 } + 3$ 
D)  It is the graph of $f ( x ) = \sqrt { x }$ translated 4 units to the right, shrunken vertically by a factor of $\frac { 1 } { 2 }$ and translated 3 units up. The equation is $\mathrm { y } = \frac { 1 } { 2 } \sqrt { x - 4 } + 3$ 
A)  It is the graph of $f ( x ) = \sqrt { x }$ translated 4 units to the right, shrunken vertically by a factor of $\frac { 1 } { 2 }$ and translated 3 units up. The equation is $y = \frac { 1 } { 2 } \sqrt { x + 4 } + 3$ 
B)  It is the graph of $\mathrm { f } ( \mathrm { x } ) = \sqrt { \mathrm { x } }$ translated 4 units to the right, stretched vertically by a factor of 2 and translated 3 units up. The equation is $y = 2 \sqrt { x - 4 } + 3$ 
C)  It is the graph of $f ( x ) = \sqrt { x }$ translated 4 units to the right, stretched vertically by a factor of 2 and translated 3 units up. The equation is $y = 2 \sqrt { x + 4 } + 3$ 
D)  It is the graph of $f ( x ) = \sqrt { x }$ translated 4 units to the right, shrunken vertically by a factor of $\frac { 1 } { 2 }$ and translated 3 units up. The equation is $\mathrm { y } = \frac { 1 } { 2 } \sqrt { x - 4 } + 3$

Question 11

Decide whether the relation defines a function.
-

Accepted Answer

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

Question 12

Determine if the function is even, odd, or neither.
-$f ( x ) = - 5 x ^ { 3 } + 9 x$

Accepted Answer

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

Question 13

Consider the function h as defined. Find functions f and g so tha $( f \circ g ) ( x ) = h ( x )$
-$$h ( x ) = \frac { 1 } { x ^ { 2 } - 6 }$$

Accepted Answer

A)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = x - 6$ 
B)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = - \frac { 1 } { 6 }$ 
C)  $f ( x ) = \frac { 1 } { x } , g ( x ) = x ^ { 2 } - 6$ 
D)  $f ( x ) = \frac { 1 } { 6 } , g ( x ) = x ^ { 2 } - 6$ 
A)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = x - 6$ 
B)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = - \frac { 1 } { 6 }$ 
C)  $f ( x ) = \frac { 1 } { x } , g ( x ) = x ^ { 2 } - 6$ 
D)  $f ( x ) = \frac { 1 } { 6 } , g ( x ) = x ^ { 2 } - 6$

Question 14

For the given functions f and g , find the indicated composition.
-$$f ( x ) = - 4 x + 9 , \quad g ( x ) = 5 x + 3$$
$( g f ) ( x )$

Accepted Answer

A)  $- 20 x + 21$ 
B)  $20 x + 48$ 
C)  $- 20 x - 42$ 
D)  $- 20 x + 48$ 
A)  $- 20 x + 21$ 
B)  $20 x + 48$ 
C)  $- 20 x - 42$ 
D)  $- 20 x + 48$

Question 15

For the points P and Q, find the coordinates of the midpoint of the segment PQ.
-$$P ( 0 , - 1 ) , Q ( 8,8 )$$

Accepted Answer

A)  $( 8,7 )$ 
B)  $\left( - 4 , - \frac { 9 } { 2 } \right)$ 
C)  $( - 8 , - 9 )$ 
D)  $\left( 4 , \frac { 7 } { 2 } \right)$ 
A)  $( 8,7 )$ 
B)  $\left( - 4 , - \frac { 9 } { 2 } \right)$ 
C)  $( - 8 , - 9 )$ 
D)  $\left( 4 , \frac { 7 } { 2 } \right)$

Question 16

The graph of y = f(x) is given. Use the graph to find the function value.
-Find f(-2).

Accepted Answer

A)  5 
B)  2 
C)  $- 2$ 
D)  $1.25$ 
A)  5 
B)  2 
C)  $- 2$ 
D)  $1.25$

Question 17

Graph the line described.
-through $( 0,3 ) ; m = - 2$

Accepted Answer

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

Question 18

Suppose the point (2, 4) is on the graph of y $y = f ( x )$ . Find a point on the graph of the given function.
-$y = 3 f ( x )$

Accepted Answer

A)  (5, 2) 
B)  (2, 6) 
C)  (6, 4) 
D)  (2, 12) 
A)  (5, 2) 
B)  (2, 6) 
C)  (6, 4) 
D)  (2, 12)

Question 19

Find the average rate of change illustrated in the graph.
-A faucet is used to add water to a large bottle that already contained some water. After it has been filling for 5 seconds, the gauge on the bottle indicates that it contains 25 ounces of water. After it has been filling for 12
Seconds, the gauge indicates the bottle contains 53 ounces of water. Find and interpret the average rate of
Change in the volume of water per second.

Accepted Answer

A)  $\frac { 1 } { 4 }$ ounce per second; the average rate of change in the volume of water is $\frac { 1 } { 4 }$ ounce per second. 
B)  41 ounces per second; the average rate of change in the volume of water is 41 ounces per second. 
C)  4 ounces per second; the average rate of change in the volume of water is 4 ounces per second. 
D)  5 ounces per second; the average rate of change in the volume of water is 5 ounces per second. 
A)  $\frac { 1 } { 4 }$ ounce per second; the average rate of change in the volume of water is $\frac { 1 } { 4 }$ ounce per second. 
B)  41 ounces per second; the average rate of change in the volume of water is 41 ounces per second. 
C)  4 ounces per second; the average rate of change in the volume of water is 4 ounces per second. 
D)  5 ounces per second; the average rate of change in the volume of water is 5 ounces per second.

Question 20

Find the requested value.
-$f ( - 3 )$ for $f ( x ) = \left\{ \begin{array} { l l } 3 x , & \text { if } x \leq - 1 \ x - 2 , & \text { if } x > - 1 \end{array} \right.$

Accepted Answer

A)  $- 5$ 
B)  9 
C)  1 
D)  $- 9$ 
A)  $- 5$ 
B)  9 
C)  1 
D)  $- 9$

Give the domain and range of the relation. -

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = \sqrt { 6 x - 9 } , g ( x ) = \frac { 1 } { x }$ Find $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } )$

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - $x ^ { 2 } + y ^ { 2 } - 8 x + 12 y - 29 = 0$

Give a rule for the piecewise-defined function. Then give the domain and range. -

Select the equation that describes the graph shown.

Graph the circle. - $(x-2)^{2}+(y-4)^{2}=9$ $Graph the circle. - (x-2)^{2}+(y-4)^{2}=9$

Match the description with the correct symbolic expression. -a linear function whose graph has a slope of 8

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint (c, y), endpoint (m, q)

Graph the line described. - $\text { through } ( 0,4 ) ; \mathrm { m } = - \frac { 1 } { 6 }$ $Graph the line described. - \text { through } ( 0,4 ) ; \mathrm { m } = - \frac { 1 } { 6 }$

Describe the transformations and give the equation for the graph. -

Decide whether the relation defines a function. -

Determine if the function is even, odd, or neither. - $f ( x ) = - 5 x ^ { 3 } + 9 x$

Consider the function h as defined. Find functions f and g so tha $( f \circ g ) ( x ) = h ( x )$ - $h ( x ) = \frac { 1 } { x ^ { 2 } - 6 }$

For the given functions f and g , find the indicated composition. - $f ( x ) = - 4 x + 9 , \quad g ( x ) = 5 x + 3$ $( g f ) ( x )$

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $P ( 0 , - 1 ) , Q ( 8,8 )$

The graph of y = f(x) is given. Use the graph to find the function value. -Find f(-2).

Graph the line described. -through $( 0,3 ) ; m = - 2$

Suppose the point (2, 4) is on the graph of y $y = f ( x )$ . Find a point on the graph of the given function. - $y = 3 f ( x )$

Find the requested value. - $f ( - 3 )$ for $f ( x ) = \left\{ \begin{array} { l l } 3 x , & \text { if } x \leq - 1 \\ x - 2 , & \text { if } x > - 1 \end{array} \right.$

Review of Basic Concepts

Equations and Inequalities

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 3: Graphs and Functions

Give the domain and range of the relation. -

For the pair of functions, find the indicated sum, difference, product, or quotient. - f(x)=6x−9,g(x)=1xf ( x ) = \sqrt { 6 x - 9 } , g ( x ) = \frac { 1 } { x }f(x)=6x−9​,g(x)=x1​ Find (fg)(x)\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } )(gf​)(x)

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - x2+y2−8x+12y−29=0x ^ { 2 } + y ^ { 2 } - 8 x + 12 y - 29 = 0x2+y2−8x+12y−29=0

Give a rule for the piecewise-defined function. Then give the domain and range. -

Select the equation that describes the graph shown.

Graph the circle. - (x−2)2+(y−4)2=9(x-2)^{2}+(y-4)^{2}=9(x−2)2+(y−4)2=9

Match the description with the correct symbolic expression. -a linear function whose graph has a slope of 8

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint (c, y), endpoint (m, q)

Graph the line described. - through (0,4);m=−16\text { through } ( 0,4 ) ; \mathrm { m } = - \frac { 1 } { 6 } through (0,4);m=−61​

Describe the transformations and give the equation for the graph. -

Decide whether the relation defines a function. -

Determine if the function is even, odd, or neither. - f(x)=−5x3+9xf ( x ) = - 5 x ^ { 3 } + 9 xf(x)=−5x3+9x

Consider the function h as defined. Find functions f and g so tha (f∘g)(x)=h(x)( f \circ g ) ( x ) = h ( x )(f∘g)(x)=h(x) - h(x)=1x2−6h ( x ) = \frac { 1 } { x ^ { 2 } - 6 }h(x)=x2−61​

For the given functions f and g , find the indicated composition. - f(x)=−4x+9,g(x)=5x+3f ( x ) = - 4 x + 9 , \quad g ( x ) = 5 x + 3f(x)=−4x+9,g(x)=5x+3 (gf)(x)( g f ) ( x )(gf)(x)

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - P(0,−1),Q(8,8)P ( 0 , - 1 ) , Q ( 8,8 )P(0,−1),Q(8,8)

The graph of y = f(x) is given. Use the graph to find the function value. -Find f(-2).

Graph the line described. -through (0,3);m=−2( 0,3 ) ; m = - 2(0,3);m=−2

Suppose the point (2, 4) is on the graph of y y=f(x)y = f ( x )y=f(x) . Find a point on the graph of the given function. - y=3f(x)y = 3 f ( x )y=3f(x)

Find the requested value. - f(−3)f ( - 3 )f(−3) for f(x)={3x, if x≤−1x−2, if x>−1f ( x ) = \left\{ \begin{array} { l l } 3 x , & \text { if } x \leq - 1 \\ x - 2 , & \text { if } x > - 1 \end{array} \right.f(x)={3x,x−2,​ if x≤−1 if x>−1​

Review of Basic Concepts

Equations and Inequalities

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = \sqrt { 6 x - 9 } , g ( x ) = \frac { 1 } { x }$ Find $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } )$

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - $x ^ { 2 } + y ^ { 2 } - 8 x + 12 y - 29 = 0$

Graph the circle. - $(x-2)^{2}+(y-4)^{2}=9$ $Graph the circle. - (x-2)^{2}+(y-4)^{2}=9$

Graph the line described. - $\text { through } ( 0,4 ) ; \mathrm { m } = - \frac { 1 } { 6 }$ $Graph the line described. - \text { through } ( 0,4 ) ; \mathrm { m } = - \frac { 1 } { 6 }$

Determine if the function is even, odd, or neither. - $f ( x ) = - 5 x ^ { 3 } + 9 x$

Consider the function h as defined. Find functions f and g so tha $( f \circ g ) ( x ) = h ( x )$ - $h ( x ) = \frac { 1 } { x ^ { 2 } - 6 }$

For the given functions f and g , find the indicated composition. - $f ( x ) = - 4 x + 9 , \quad g ( x ) = 5 x + 3$ $( g f ) ( x )$

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $P ( 0 , - 1 ) , Q ( 8,8 )$

Graph the line described. -through $( 0,3 ) ; m = - 2$

Suppose the point (2, 4) is on the graph of y $y = f ( x )$ . Find a point on the graph of the given function. - $y = 3 f ( x )$

Find the requested value. - $f ( - 3 )$ for $f ( x ) = \left\{ \begin{array} { l l } 3 x , & \text { if } x \leq - 1 \\ x - 2 , & \text { if } x > - 1 \end{array} \right.$