Question 1

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

Accepted Answer

A) $\text { } f(x)=\left\{\begin{array}{ll} -6 & \text { if } x \leq-2 \ -1 & \text { if } x>-2 \end{array} ; \text { Domain: }(\infty, \infty) \text {, Range: }\{-6,-1\}\right.$ B) $f ( x ) = \left\{ \begin{array} { l l } - 6 & \text { if } x - 2 \end{array} ; \right.$ Domain: $\{ - 6 , - 1 \}$, Range: $( \infty , \infty )$ D) $f ( x ) = \left\{ \begin{array} { l l } - 6 & \text { if } x < - 2 \ - 1 & \text { if } x \geq - 2 \end{array} ; \right.$ Domain: $( \infty , \infty )$, Range: $\{ - 6 , - 1 \}$ A) $\text { } f(x)=\left\{\begin{array}{ll} -6 & \text { if } x \leq-2 \ -1 & \text { if } x>-2 \end{array} ; \text { Domain: }(\infty, \infty) \text {, Range: }\{-6,-1\}\right.$ B) $f ( x ) = \left\{ \begin{array} { l l } - 6 & \text { if } x - 2 \end{array} ; \right.$ Domain: $\{ - 6 , - 1 \}$, Range: $( \infty , \infty )$ D) $f ( x ) = \left\{ \begin{array} { l l } - 6 & \text { if } x < - 2 \ - 1 & \text { if } x \geq - 2 \end{array} ; \right.$ Domain: $( \infty , \infty )$, Range: $\{ - 6 , - 1 \}$

Question 2

Decide whether the relation defines a function.
-

Accepted Answer

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

Question 3

Match the equation with the correct graph.
-$$y = 3$$

Accepted Answer

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

Question 4

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such.
-$h(x)=4$

Accepted Answer

A)  $\mathrm { D } = \{ 4 \} , \mathrm { R } = ( - \infty , \infty )$
constant function 
  
B)  $\mathrm { D } = \{ 4 \} , \mathrm { R } = ( - \infty , \infty )$
constant function
  
C)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = \{ 4 \}$
constant function
  
D)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = \{ 4 \}$
 constant function 
  
A)  $\mathrm { D } = \{ 4 \} , \mathrm { R } = ( - \infty , \infty )$
constant function 
  
B)  $\mathrm { D } = \{ 4 \} , \mathrm { R } = ( - \infty , \infty )$
constant function
  
C)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = \{ 4 \}$
constant function
  
D)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = \{ 4 \}$
 constant function

Question 5

The graph of y = f(x) is given. Use the graph to find the function value.
- 
Find $f ( - 4 )$.

Accepted Answer

A)  1 
B)  $- 4$ 
C)  $1.8$ 
D)  None of these 
A)  1 
B)  $- 4$ 
C)  $1.8$ 
D)  None of these

Question 6

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.
-$$y = - 5 x ^ { 3 } + 5 x$$

Accepted Answer

A)  $x$-axis only 
B)  origin only 
C)  $x$-axis, $y$-axis, origin 
D)  $y$-axis only 
A)  $x$-axis only 
B)  origin only 
C)  $x$-axis, $y$-axis, origin 
D)  $y$-axis only

Question 7

Find the center-radius form of the equation of the circle.
-center $( 4,0 )$, radius $\sqrt { 7 }$

Accepted Answer

A)  $( x - 4 ) ^ { 2 } + y ^ { 2 } = 7$ 
B)  $( x - 4 ) ^ { 2 } + y ^ { 2 } = \sqrt { 7 }$ 
C)  $( x + 4 ) ^ { 2 } + y ^ { 2 } = 7$ 
D)  $x ^ { 2 } + ( y - 4 ) ^ { 2 } = 49$ 
A)  $( x - 4 ) ^ { 2 } + y ^ { 2 } = 7$ 
B)  $( x - 4 ) ^ { 2 } + y ^ { 2 } = \sqrt { 7 }$ 
C)  $( x + 4 ) ^ { 2 } + y ^ { 2 } = 7$ 
D)  $x ^ { 2 } + ( y - 4 ) ^ { 2 } = 49$

Question 8

The locations of three receiving stations and the distances to the epicenter of an earthquake are contained in the following three equations: $( x + 5 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 4 , ( x + 7 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 4 , ( x - 1 ) ^ { 2 } + ( y + 13 ) ^ { 2 } = 100$. Determine the location of the epicenter.

Accepted Answer

A)  at $( - 4 , - 6 )$ 
B)  at $( - 4 , - 5 )$ 
C)  at $( - 6 , - 3 )$ 
D)  at $( - 5 , - 5 )$ 
A)  at $( - 4 , - 6 )$ 
B)  at $( - 4 , - 5 )$ 
C)  at $( - 6 , - 3 )$ 
D)  at $( - 5 , - 5 )$

Question 9

Determine whether the three points are the vertices of a right triangle.
-$( 3 , - 9 ) , ( 10 , - 9 ) , ( 10 , - 1 )$

Accepted Answer

A) True 
 B)False

Question 10

Graph the line and give the domain and the range.
-$3 x-6 y=18$

Accepted Answer

A)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
B)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
C)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
D)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
A)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
B)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
C)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
D)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$

Question 11

For the points P and Q, find the distance d(P, Q).
-$\mathrm { P } ( 7 , - 2 ) , \mathrm { Q } ( 5,2 )$

Accepted Answer

A)  6 
B)  $2 \sqrt { 5 }$ 
C)  $12 \sqrt { 3 }$ 
D)  12 
A)  6 
B)  $2 \sqrt { 5 }$ 
C)  $12 \sqrt { 3 }$ 
D)  12

Question 12

Select the equation that describes the graph shown.

Accepted Answer

A)  $y = \sqrt { x } - 3$ 
B)  $y = \sqrt { x + 1 } + 3$ 
C)  $y = \sqrt { x - 1 } - 3$ 
D)  $y = \sqrt { x + 1 } - 3$ 
A)  $y = \sqrt { x } - 3$ 
B)  $y = \sqrt { x + 1 } + 3$ 
C)  $y = \sqrt { x - 1 } - 3$ 
D)  $y = \sqrt { x + 1 } - 3$

Question 13

Graph the equation by plotting points.
-$y=x^{2}-1$

Accepted Answer

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

Question 14

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

Accepted Answer

A)  It is the graph of $f ( x ) = \sqrt { x }$ translated 8 units to the left and translated 5 units up. The equation is $y =$ $\sqrt { x - 8 } - 5$ 
B)  It is the graph of $f ( x ) = \sqrt { x }$ translated 8 units to the left and translated 5 units up. The equation is $y =$ $\sqrt { x - 8 } + 5$ 
C)  It is the graph of $f ( x ) = \sqrt { x }$ translated 8 units to the left and translated 5 units up. The equation is $y =$ $\sqrt { x + 8 } + 5$ 
D)  It is the graph of $f ( x ) = \sqrt { x }$ translated 8 units to the left and translated 5 units up. The equation is $y =$ $\sqrt { x + 8 } - 5$ 
A)  It is the graph of $f ( x ) = \sqrt { x }$ translated 8 units to the left and translated 5 units up. The equation is $y =$ $\sqrt { x - 8 } - 5$ 
B)  It is the graph of $f ( x ) = \sqrt { x }$ translated 8 units to the left and translated 5 units up. The equation is $y =$ $\sqrt { x - 8 } + 5$ 
C)  It is the graph of $f ( x ) = \sqrt { x }$ translated 8 units to the left and translated 5 units up. The equation is $y =$ $\sqrt { x + 8 } + 5$ 
D)  It is the graph of $f ( x ) = \sqrt { x }$ translated 8 units to the left and translated 5 units up. The equation is $y =$ $\sqrt { x + 8 } - 5$

Question 15

Decide whether the relation defines a function.
-

Accepted Answer

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

Question 16

Find the requested value.
-$$\begin{array}{l}
\text { Using the given tables, find } ( g a ) ( 3 )\
\begin{array} { l | l | r | r | r l } 
x & 3 & 6 & 4 & 8 \
\hline f ( x ) & 4 & 6 & 13 & 15
\end{array} \quad \begin{array} { l | l | l | l | l } 
x & 5 & 8 & 3 & 4 \
\hline g ( x ) & 9 & 5 & 8 & 7
\end{array}
\end{array}$$

Accepted Answer

A)  13 
B)  7 
C)  5 
D)  15 
A)  13 
B)  7 
C)  5 
D)  15

Question 17

Give the domain and range of the relation.
-

Accepted Answer

A)  domain: {4, 12}; range: {5, 13} 
B)  None of these 
C)  domain: {5, 8, 13}; range: {4, 7, 12} 
D)  domain: {4, 7, 12}; range: {5, 8, 13} 
A)  domain: {4, 12}; range: {5, 13} 
B)  None of these 
C)  domain: {5, 8, 13}; range: {4, 7, 12} 
D)  domain: {4, 7, 12}; range: {5, 8, 13}

Question 18

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 right, reflected across the $y$-axis and translated 2 units down. The equation is $y = \sqrt { - x - 3 } - 2$ 
B)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the right, reflected across the $x$-axis and translated 2 units down. The equation is $y = \sqrt { - x + 3 } - 2$ 
C)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the right, reflected across the $x$-axis and translated 2 units down. The equation is $y = - \sqrt { x + 3 } - 2$ 
D)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the right, reflected across the $x$-axis and translated 2 units down. The equation is $y = - \sqrt { x - 3 } - 2$ 
A)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the right, reflected across the $y$-axis and translated 2 units down. The equation is $y = \sqrt { - x - 3 } - 2$ 
B)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the right, reflected across the $x$-axis and translated 2 units down. The equation is $y = \sqrt { - x + 3 } - 2$ 
C)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the right, reflected across the $x$-axis and translated 2 units down. The equation is $y = - \sqrt { x + 3 } - 2$ 
D)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the right, reflected across the $x$-axis and translated 2 units down. The equation is $y = - \sqrt { x - 3 } - 2$

Question 19

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph.
-$$5 x ^ { 2 } + 5 y ^ { 2 } + 40 x - 30 y + 120 = 0$$

Accepted Answer

A)  no; the graph is the point $( - 4,3 )$ 
B)  no; the graph is the point $( 4 , - 3 )$ 
C)  no; the graph is nonexistent 
D)  yes 
A)  no; the graph is the point $( - 4,3 )$ 
B)  no; the graph is the point $( 4 , - 3 )$ 
C)  no; the graph is nonexistent 
D)  yes

Question 20

Give the domain and range of the relation.
-$$y = \sqrt { 3 + x }$$

Accepted Answer

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

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

Decide whether the relation defines a function. -

Match the equation with the correct graph. - $y = 3$

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - $h(x)=4$

The graph of y = f(x) is given. Use the graph to find the function value. - Find $f ( - 4 )$ .

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. - $y = - 5 x ^ { 3 } + 5 x$

Find the center-radius form of the equation of the circle. -center $( 4,0 )$ , radius $\sqrt { 7 }$

Determine whether the three points are the vertices of a right triangle. - $( 3 , - 9 ) , ( 10 , - 9 ) , ( 10 , - 1 )$

Graph the line and give the domain and the range. - $3 x-6 y=18$

For the points P and Q, find the distance d(P, Q). - $\mathrm { P } ( 7 , - 2 ) , \mathrm { Q } ( 5,2 )$

Select the equation that describes the graph shown.

Graph the equation by plotting points. - $y=x^{2}-1$ $Graph the equation by plotting points. - y=x^{2}-1$

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

Decide whether the relation defines a function. -

Find the requested value. - Using the given tables, find (ga)(3) x 3 6 4 8 f(x) 4 6 13 15 x 5 8 3 4 g(x) 9 5 8 7

Give the domain and range of the relation. -

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

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - $5 x ^ { 2 } + 5 y ^ { 2 } + 40 x - 30 y + 120 = 0$

Give the domain and range of the relation. - $y = \sqrt { 3 + x }$

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

Decide whether the relation defines a function. -

Match the equation with the correct graph. - y=3y = 3y=3

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - h(x)=4h(x)=4h(x)=4

The graph of y = f(x) is given. Use the graph to find the function value. - Find f(−4)f ( - 4 )f(−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=−5x3+5xy = - 5 x ^ { 3 } + 5 xy=−5x3+5x

Find the center-radius form of the equation of the circle. -center (4,0)( 4,0 )(4,0) , radius 7\sqrt { 7 }7​

Determine whether the three points are the vertices of a right triangle. - (3,−9),(10,−9),(10,−1)( 3 , - 9 ) , ( 10 , - 9 ) , ( 10 , - 1 )(3,−9),(10,−9),(10,−1)

Graph the line and give the domain and the range. - 3x−6y=183 x-6 y=183x−6y=18

For the points P and Q, find the distance d(P, Q). - P(7,−2),Q(5,2)\mathrm { P } ( 7 , - 2 ) , \mathrm { Q } ( 5,2 )P(7,−2),Q(5,2)

Select the equation that describes the graph shown.

Graph the equation by plotting points. - y=x2−1y=x^{2}-1y=x2−1

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

Decide whether the relation defines a function. -

Find the requested value. - Using the given tables, find (ga)(3) x 3 6 4 8 f(x) 4 6 13 15 x 5 8 3 4 g(x) 9 5 8 7

Give the domain and range of the relation. -

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

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - 5x2+5y2+40x−30y+120=05 x ^ { 2 } + 5 y ^ { 2 } + 40 x - 30 y + 120 = 05x2+5y2+40x−30y+120=0

Give the domain and range of the relation. - y=3+xy = \sqrt { 3 + x }y=3+x​

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

Match the equation with the correct graph. - $y = 3$

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - $h(x)=4$

The graph of y = f(x) is given. Use the graph to find the function value. - Find $f ( - 4 )$ .

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. - $y = - 5 x ^ { 3 } + 5 x$

Find the center-radius form of the equation of the circle. -center $( 4,0 )$ , radius $\sqrt { 7 }$

Determine whether the three points are the vertices of a right triangle. - $( 3 , - 9 ) , ( 10 , - 9 ) , ( 10 , - 1 )$

Graph the line and give the domain and the range. - $3 x-6 y=18$

For the points P and Q, find the distance d(P, Q). - $\mathrm { P } ( 7 , - 2 ) , \mathrm { Q } ( 5,2 )$

Graph the equation by plotting points. - $y=x^{2}-1$ $Graph the equation by plotting points. - y=x^{2}-1$

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - $5 x ^ { 2 } + 5 y ^ { 2 } + 40 x - 30 y + 120 = 0$

Give the domain and range of the relation. - $y = \sqrt { 3 + x }$