Question 1

Find the specified domain.
-Use the graphs to find the value of $( f - g ) ( - 1 )$.

Accepted Answer

A)  3 
B)  $- 1$ 
C)  0 
D)  1 
A)  3 
B)  $- 1$ 
C)  0 
D)  1

Question 2

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

Accepted Answer

A)  $( 5,4 )$ 
B)  $( 2,7 )$ 
C)  $( - 1,4 )$ 
D)  $( 2,1 )$ 
A)  $( 5,4 )$ 
B)  $( 2,7 )$ 
C)  $( - 1,4 )$ 
D)  $( 2,1 )$

Question 3

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

Accepted Answer

A)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the left and translated 2 units up. The equation is $y = \sqrt { x - 3 } - 2$ 
B)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the left and translated 2 units up. The equation is $y = \sqrt { x + 3 } + 2$ 
C)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the left and translated 2 units up. The equation is $y = \sqrt { x + 3 } - 2$ 
D)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the left and translated 2 units up. The equation is $y = \sqrt { x - 3 } + 2$ 
A)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the left and translated 2 units up. The equation is $y = \sqrt { x - 3 } - 2$ 
B)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the left and translated 2 units up. The equation is $y = \sqrt { x + 3 } + 2$ 
C)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the left and translated 2 units up. The equation is $y = \sqrt { x + 3 } - 2$ 
D)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the left and translated 2 units up. The equation is $y = \sqrt { x - 3 } + 2$

Question 4

Determine if the function is even, odd, or neither.
-$f ( x ) = - 4 x ^ { 3 } + 9 x$

Accepted Answer

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

Question 5

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 14 ounces of water. After it has been filling for 13 seconds, the gauge indicates the bottle contains 30 ounces of water. Find and interpret the average rate of change in the volume of water per second.

Accepted Answer

A)  4 ounces per second; the average rate of change in the volume of water is 4 ounces per second. 
B)  17 ounces per second; the average rate of change in the volume of water is 17 ounces per second. 
C)  2 ounces per second; the average rate of change in the volume of water is 2 ounces per second. 
D)  $\frac { 1 } { 2 }$ ounce per second; the average rate of change in the volume of water is $\frac { 1 } { 2 }$ ounce per second. 
A)  4 ounces per second; the average rate of change in the volume of water is 4 ounces per second. 
B)  17 ounces per second; the average rate of change in the volume of water is 17 ounces per second. 
C)  2 ounces per second; the average rate of change in the volume of water is 2 ounces per second. 
D)  $\frac { 1 } { 2 }$ ounce per second; the average rate of change in the volume of water is $\frac { 1 } { 2 }$ ounce per second.

Question 6

Find the slope of the line and sketch the graph.
-$$y = - 5 x - 1$$

Accepted Answer

A)  $m = - \frac { 1 } { 5 }$
  
B)  $m = 5$
  
C)  $m = - 5$
  
D)  $m = - 1$
  
A)  $m = - \frac { 1 } { 5 }$
  
B)  $m = 5$
  
C)  $m = - 5$
  
D)  $m = - 1$

Question 7

Graph the point symmetric to the given point.
-

Accepted Answer

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

Question 8

Determine whether (f  g)(x) = x and whether (g  f)(x) = x.
-$$f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 }$$

Accepted Answer

A)  Yes, no 
B)  No, yes 
C)  No, no 
D)  Yes, yes 
A)  Yes, no 
B)  No, yes 
C)  No, no 
D)  Yes, yes

Question 9

For the pair of functions, find the indicated sum, difference, product, or quotient.
-$$f ( x ) = 7 x - 2 , g ( x ) = 8 x + 6$$
Find $( f g ) ( x )$.

Accepted Answer

A)  $56 x ^ { 2 } + 26 x - 12$ 
B)  $56 x ^ { 2 } - 10 x - 12$ 
C)  $56 x ^ { 2 } - 12$ 
D)  $15 x ^ { 2 } + 26 x + 4$ 
A)  $56 x ^ { 2 } + 26 x - 12$ 
B)  $56 x ^ { 2 } - 10 x - 12$ 
C)  $56 x ^ { 2 } - 12$ 
D)  $15 x ^ { 2 } + 26 x + 4$

Question 10

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

Accepted Answer

A)  $( 2,4 )$ 
B)  $( 2 , - 4 )$ 
C)  $( - 2 , - 4 )$ 
D)  $( - 2,4 )$ 
A)  $( 2,4 )$ 
B)  $( 2 , - 4 )$ 
C)  $( - 2 , - 4 )$ 
D)  $( - 2,4 )$

Question 11

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-midpoint (5, 9), endpoint (2, 4)

Accepted Answer

A)  (12, 10) 
B)  (8, -1) 
C)  (8, 14) 
D)  (-4, -6) 
A)  (12, 10) 
B)  (8, -1) 
C)  (8, 14) 
D)  (-4, -6)

Question 12

Determine whether the equation has a graph that is symmetric with respect to the y-axis, the x-axis, the origin, or none of
these.
-$$y = ( x - 6 ) ( x - 6 )$$

Accepted Answer

A)  $x$-axis only 
B)  $y$-axis only 
C)  $x$-axis, $y$-axis, origin 
D)  none of these 
A)  $x$-axis only 
B)  $y$-axis only 
C)  $x$-axis, $y$-axis, origin 
D)  none of these

Question 13

Graph the function.
-$f(x)=x^{3}-1$

Accepted Answer

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

Question 14

Find the requested function value.
-Find $( g \circ f ) ( 6 )$ when $f ( x ) = - 5 x + 5$ and $g ( x ) = - 7 x ^ { 2 } - 4 x + 5$

Accepted Answer

A)  $- 4270$ 
B)  280 
C)  310 
D)  1360 
A)  $- 4270$ 
B)  280 
C)  310 
D)  1360

Question 15

Describe the transformations and give the equation for the graph.
-Find $( f g ) ( - 2 )$ when $f ( x ) = x + 1$ and $g ( x ) = - 5 x ^ { 2 } + 11 x + 4$

Accepted Answer

A)  14 
B)  48 
C)  114 
D)  38 
A)  14 
B)  48 
C)  114 
D)  38

Question 16

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph.
-$$2 x ^ { 2 } + 2 y ^ { 2 } + 16 x - 4 y + 26 = 0$$

Accepted Answer

A)  no; the graph is the point $( 4 , - 1 )$ 
B)  yes 
C)  no; the graph is the point $( - 4,1 )$ 
D)  no; the graph is nonexistent 
A)  no; the graph is the point $( 4 , - 1 )$ 
B)  yes 
C)  no; the graph is the point $( - 4,1 )$ 
D)  no; the graph is nonexistent

Question 17

Determine whether the three points are collinear.
-(0, -12), (-1, -3), (-9, -11)

Accepted Answer

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

Question 18

Find the center-radius form of the equation of the circle.
-center $( 6,0 )$, radius 3

Accepted Answer

A)  $x ^ { 2 } + ( y - 6 ) ^ { 2 } = 3$ 
B)  $( x + 6 ) ^ { 2 } + y ^ { 2 } = 9$ 
C)  $( x - 6 ) ^ { 2 } + y ^ { 2 } = 9$ 
D)  $x ^ { 2 } + ( y + 6 ) ^ { 2 } = 3$ 
A)  $x ^ { 2 } + ( y - 6 ) ^ { 2 } = 3$ 
B)  $( x + 6 ) ^ { 2 } + y ^ { 2 } = 9$ 
C)  $( x - 6 ) ^ { 2 } + y ^ { 2 } = 9$ 
D)  $x ^ { 2 } + ( y + 6 ) ^ { 2 } = 3$

Question 19

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

Question 20

Find the center-radius form of the circle described or graphed.
-a circle having a diameter with endpoints $( - 6 , - 7 )$ and $( - 1,2 )$

Accepted Answer

A)  $\left( x - \frac { 7 } { 2 } \right) ^ { 2 } + \left( y - \frac { 5 } { 2 } \right) ^ { 2 } = 74$ 
B)  $\left( x - \frac { 7 } { 2 } \right) ^ { 2 } + \left( y + \frac { 5 } { 2 } \right) ^ { 2 } = 130$ 
C)  $\left( x + \frac { 5 } { 2 } \right) ^ { 2 } + \left( y + \frac { 9 } { 2 } \right) ^ { 2 } = 106$ 
D)  $\left( x + \frac { 7 } { 2 } \right) ^ { 2 } + \left( y + \frac { 5 } { 2 } \right) ^ { 2 } = \frac { 53 } { 2 }$ 
A)  $\left( x - \frac { 7 } { 2 } \right) ^ { 2 } + \left( y - \frac { 5 } { 2 } \right) ^ { 2 } = 74$ 
B)  $\left( x - \frac { 7 } { 2 } \right) ^ { 2 } + \left( y + \frac { 5 } { 2 } \right) ^ { 2 } = 130$ 
C)  $\left( x + \frac { 5 } { 2 } \right) ^ { 2 } + \left( y + \frac { 9 } { 2 } \right) ^ { 2 } = 106$ 
D)  $\left( x + \frac { 7 } { 2 } \right) ^ { 2 } + \left( y + \frac { 5 } { 2 } \right) ^ { 2 } = \frac { 53 } { 2 }$

Find the specified domain. -Use the graphs to find the value of $( f - g ) ( - 1 )$ .

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

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

Determine if the function is even, odd, or neither. - $f ( x ) = - 4 x ^ { 3 } + 9 x$

Find the slope of the line and sketch the graph. - $y = - 5 x - 1$

Graph the point symmetric to the given point. -

Determine whether (f  g)(x) = x and whether (g  f)(x) = x. - $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 }$

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = 7 x - 2 , g ( x ) = 8 x + 6$ Find $( f g ) ( x )$ .

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

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint (5, 9), endpoint (2, 4)

Determine whether the equation has a graph that is symmetric with respect to the y-axis, the x-axis, the origin, or none of these. - $y = ( x - 6 ) ( x - 6 )$

Graph the function. - $f(x)=x^{3}-1$ $Graph the function. - f(x)=x^{3}-1$

Find the requested function value. -Find $( g \circ f ) ( 6 )$ when $f ( x ) = - 5 x + 5$ and $g ( x ) = - 7 x ^ { 2 } - 4 x + 5$

Describe the transformations and give the equation for the graph. -Find $( f g ) ( - 2 )$ when $f ( x ) = x + 1$ and $g ( x ) = - 5 x ^ { 2 } + 11 x + 4$

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - $2 x ^ { 2 } + 2 y ^ { 2 } + 16 x - 4 y + 26 = 0$

Determine whether the three points are collinear. -(0, -12), (-1, -3), (-9, -11)

Find the center-radius form of the equation of the circle. -center $( 6,0 )$ , radius 3

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

Find the center-radius form of the circle described or graphed. -a circle having a diameter with endpoints $( - 6 , - 7 )$ and $( - 1,2 )$

Review of Basic Concepts

Equations and Inequalities

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 3: Graphs and Functions

Find the specified domain. -Use the graphs to find the value of (f−g)(−1)( f - g ) ( - 1 )(f−g)(−1) .

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