Question 1

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-A equation in the variables x and y can be written in the form Ax + By = C, where A
and B are not both zero.

Accepted Answer

The answer of Write the word or phrase that best...

Question 2

Determine if the given points form the vertices of a right triangle.
-(-3, 5), (-1, 3), and (-4, 0)

Accepted Answer

A)  No 
B)  Yes

Question 3

Determine which of the given points are solutions to the given equation.
-$2 x ^ { 2 } + y = 4$
I. $( 3 , - 14 )$
II. $( - 3,14 )$ III. $( - 3 , - 14 )$

Accepted Answer

A)  III 
B)  $\mathrm { I }$ 
C)  II 
D)  I and II 
E)  I and III

Question 4

Graph the equation with a graphing utility on the given viewing window.
-$$y = 3 x - 5 \text { on } [ - 10,10,1 ] \text { by } [ - 10,10,1 ]$$

Accepted Answer

A) 
 
B)

C) 
 
D)

Question 5

Graph the function.
-$s ( x ) = \left\{ \begin{array} { l l } - x + 3 & \text { for } x \leq 3 \ \sqrt { x - 3 } & \text { for } x > 3 \end{array} \right.$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 6

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-An equation of a circle written in the form $$x ^ { 2 } + y ^ { 2 } + A x + B y + C = 0$$ = 0 is called the form of an equation of a circle.

Accepted Answer

The answer of Write the word or phrase that best...

Question 7

Identify the domain and range of the relation, and determine whether the relation is a function.
-$$\{ ( - 9,4 ) , ( - 1,2 ) , ( 18 , - 2 ) , ( - 1 , - 4 ) \}$$

Accepted Answer

A)  Domain: $\{ - 4 , - 2,2,4 \}$; Range: $\{ - 9 , - 1,18 \} ;$ Not a function 
B)  Domain: $\{ - 9 , - 1 , - 1,18 \}$; Range: $\{ - 4 , - 2,2,4 \}$; Function 
C)  Domain: $\{ - 4 , - 2,2,4 \}$; Range: $\{ - 9 , - 1,18 \}$; Function 
D)  Domain: $\{ - 9 , - 1,18 \}$; Range: $\{ - 4 , - 2,2,4 \} ;$ Not a function

Question 8

Write the domain in interval notation.
-$$h ( c ) = \frac { 2 } { \sqrt { c + 11 } - 1 }$$

Accepted Answer

A)  $( - 11 , - 10 ) \cup ( - 10 , \infty )$ 
B)  $[ - 11 , - 10 ) \cup ( - 10 , \infty )$ 
C)  $( - 11 , \infty )$ 
D)  $[ - 11 , \infty )$

Question 9

Assume that the units shown in the grid are in feet.
a. Determine the exact length and width of the rectangle shown.
b. Determine the perimeter and area.
-

Accepted Answer

A)  a. Length: $4 \mathrm { ft }$; Width: $3 \mathrm { ft }$
b. Perimeter: $14 \mathrm { ft }$; Area: $12 \mathrm { ft } ^ { 2 }$ 
B)  a. Length: $4 \sqrt { 2 } \mathrm { ft }$; Width: $3 \sqrt { 2 } \mathrm { ft }$
b. Perimeter: $7 \sqrt { 2 } \mathrm { ft }$; Area: $24 \mathrm { ft } ^ { 2 }$ 
C)  a. Length: $4 \mathrm { ft }$; Width: $3 \mathrm { ft }$
b. Perimeter: $7 \mathrm { ft }$; Area: $12 \mathrm { ft } ^ { 2 }$ 
D)  a. Length: $4 \sqrt { 2 } \mathrm { ft }$; Width: $3 \sqrt { 2 } \mathrm { ft }$
b. Perimeter: $14 \sqrt { 2 } \mathrm { ft }$; Area: $24 \mathrm { ft } ^ { 2 }$

Question 10

Evaluate the function for the given value of x.
-$g ( x ) = 4 x - 3 , h ( x ) = 3 \sqrt { x - 7 } , ( h \circ g ) ( 1 ) =$ ?

Accepted Answer

A)  $12 \sqrt { 6 } - 3$ 
B)  Undefined 
C)  $24 \sqrt { 3 } - 3$ 
D)  $3 \sqrt { 6 }$

Question 11

Find the indicated function and write its domain in interval notation.
-$$n ( x ) = x + 3 , q ( x ) = \frac { 1 } { x + 6 } , ( q \circ n ) ( x ) = ?$$

Accepted Answer

A)  $( q \circ n ) ( x ) = \frac { 1 } { x + 6 } + 3 ;$ domain: $( - \infty , 6 ) \cup ( 6 , \infty )$ 
B)  $( q \circ n ) ( x ) = \frac { 1 } { x + 9 }$; domain: $( - \infty , 9 ) \cup ( 9 , \infty )$ 
C)  $( q \circ n ) ( x ) = \frac { 1 } { x + 6 } + 3$; domain: $( - \infty , - 6 ) \cup ( - 6 , \infty )$ 
D)  $( q \circ n ) ( x ) = \frac { 1 } { x + 9 } ;$ domain: $( - \infty , - 9 ) \cup ( - 9 , \infty )$

Question 12

The graph of y = f (x) is given. Graph the indicated function.
-Graph $y = - f ( x - 2 ) - 2$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 13

Choose the one alternative that best completes the statement or answers the question.
-If bottled water costs $0.63 per bottle, then the cost, C (in dollars), for b bottles is defined by C(b) = 0.63b. How many bottles of water can be purchased for $7.56?

Accepted Answer

A)  5 bottles 
B)  16 bottles 
C)  12 bottles 
D)  8 bottles

Question 14

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-If f is defined on the interval [ $\left[ x _ { 1 } , x _ { 2 } \right]$ ], then the average rate of change of f on the interval [ $\left[ x _ { 1 } , x _ { 2 } \right]$ is
given by the formula .

Accepted Answer

The answer of Write the word or phrase that best...

Question 15

Solve the problem.
-$$\text { Use the graph of } y = b ( x ) \text { below to graph } y = b \left( \frac { 1 } { 2 } x \right) \text {. }$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 16

Find the midpoint of the line segment whose endpoints are the given points.
-$( 5.3,4.7 )$ and $( 7.2 , - 9.7 )$

Accepted Answer

A)  $( - 0.95,7.2 )$ 
B)  $( 5 , - 1.25 )$ 
C)  $( 6.25,7.2 )$ 
D)  $( 6.25 , - 2.5 )$

Question 17

Determine the slope and the y-intercept of the line.
-$$6 = - 6 y$$

Accepted Answer

A)  Slope: $1 ; y$-intercept: $( 0 , - 1 )$ 
B)  Slope: undefined; $y$-intercept: $( - 1,0 )$ 
C)  Slope: $0 ; y$-intercept: $( - 1,0 )$ 
D)  Slope: $0 ; y$-intercept: $( 0 , - 1 )$

Question 18

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-$$\text { Given a point } \left( x _ { 1 } , y _ { 1 } \right) \text { on a line with slope } m \text {, the point-slope formula is given by ـــــــــــــــــــــ}$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 19

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-A graph of an equation is symmetric with respect to the -axis
if replacing y by -y results in an equivalent equation.

Accepted Answer

The answer of Write the word or phrase that best...

Question 20

Use the graph to solve the equation and inequality. Write the solution to the inequality in interval
notation.
-a. $3 x - 3 = 2 x - 1$
b. $3 x - 3 > 2 x - 1$

Accepted Answer

A)  a. $\{ 2 \} ;$ b. $( 2 , \infty )$ 
B)  a. $\{ 2 \}$; b. $( - \infty , 2 )$ 
C)  a. $\{ 3 \}$; b. $( 3 , \infty )$ 
D)  a. $\{ 3 \}$ b. $( - \infty , 3 \}$

Exam 2: Functions and Relations

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A equation in the variables x and y can be written in the form Ax + By = C, where A and B are not both zero.

Determine if the given points form the vertices of a right triangle. -(-3, 5) , (-1, 3) , and (-4, 0)

Determine which of the given points are solutions to the given equation. - $2 x ^ { 2 } + y = 4$ I. $( 3 , - 14 )$ II. $( - 3,14 )$ III. $( - 3 , - 14 )$

Graph the equation with a graphing utility on the given viewing window. - $y = 3 x - 5 \text { on } [ - 10,10,1 ] \text { by } [ - 10,10,1 ]$

Graph the function. - $s ( x ) = \left\{ \begin{array} { l l } - x + 3 & \text { for } x \leq 3 \\ \sqrt { x - 3 } & \text { for } x > 3 \end{array} \right.$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An equation of a circle written in the form $x ^ { 2 } + y ^ { 2 } + A x + B y + C = 0$ = 0 is called the form of an equation of a circle.

Identify the domain and range of the relation, and determine whether the relation is a function. - $\{ ( - 9,4 ) , ( - 1,2 ) , ( 18 , - 2 ) , ( - 1 , - 4 ) \}$

Write the domain in interval notation. - $h ( c ) = \frac { 2 } { \sqrt { c + 11 } - 1 }$

Evaluate the function for the given value of x. - $g ( x ) = 4 x - 3 , h ( x ) = 3 \sqrt { x - 7 } , ( h \circ g ) ( 1 ) =$ ?

Find the indicated function and write its domain in interval notation. - $n ( x ) = x + 3 , q ( x ) = \frac { 1 } { x + 6 } , ( q \circ n ) ( x ) = ?$

The graph of y = f (x) is given. Graph the indicated function. -Graph $y = - f ( x - 2 ) - 2$

Choose the one alternative that best completes the statement or answers the question. -If bottled water costs $0.63 per bottle, then the cost, C (in dollars) , for b bottles is defined by C(b) = 0.63b. How many bottles of water can be purchased for $7.56?

Solve the problem. - $\text { Use the graph of } y = b ( x ) \text { below to graph } y = b \left( \frac { 1 } { 2 } x \right) \text {. }$ $Solve the problem. - \text { Use the graph of } y = b ( x ) \text { below to graph } y = b \left( \frac { 1 } { 2 } x \right) \text {. } A) B) C) D)$

Find the midpoint of the line segment whose endpoints are the given points. - $( 5.3,4.7 )$ and $( 7.2 , - 9.7 )$

Determine the slope and the y-intercept of the line. - $6 = - 6 y$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A graph of an equation is symmetric with respect to the -axis if replacing y by -y results in an equivalent equation.

Exam 2: Functions and Relations

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A equation in the variables x and y can be written in the form Ax + By = C, where A and B are not both zero.

Determine if the given points form the vertices of a right triangle. -(-3, 5) , (-1, 3) , and (-4, 0)

Determine which of the given points are solutions to the given equation. - 2x2+y=42 x ^ { 2 } + y = 42x2+y=4 I. (3,−14) ( 3 , - 14 ) (3,−14) II. (−3,14) ( - 3,14 ) (−3,14) III. (−3,−14) ( - 3 , - 14 ) (−3,−14)

Graph the equation with a graphing utility on the given viewing window. - y=3x−5 on [−10,10,1] by [−10,10,1]y = 3 x - 5 \text { on } [ - 10,10,1 ] \text { by } [ - 10,10,1 ]y=3x−5 on [−10,10,1] by [−10,10,1]

Graph the function. - s(x) ={−x+3 for x≤3x−3 for x>3s ( x ) = \left\{ \begin{array} { l l } - x + 3 & \text { for } x \leq 3 \\ \sqrt { x - 3 } & \text { for } x > 3 \end{array} \right.s(x) ={−x+3x−3​​ for x≤3 for x>3​

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An equation of a circle written in the form x2+y2+Ax+By+C=0x ^ { 2 } + y ^ { 2 } + A x + B y + C = 0x2+y2+Ax+By+C=0 = 0 is called the form of an equation of a circle.

Identify the domain and range of the relation, and determine whether the relation is a function. - {(−9,4) ,(−1,2) ,(18,−2) ,(−1,−4) }\{ ( - 9,4 ) , ( - 1,2 ) , ( 18 , - 2 ) , ( - 1 , - 4 ) \}{(−9,4) ,(−1,2) ,(18,−2) ,(−1,−4) }

Write the domain in interval notation. - h(c) =2c+11−1h ( c ) = \frac { 2 } { \sqrt { c + 11 } - 1 }h(c) =c+11​−12​

Assume that the units shown in the grid are in feet. a. Determine the exact length and width of the rectangle shown. b. Determine the perimeter and area. -

Evaluate the function for the given value of x. - g(x) =4x−3,h(x) =3x−7,(h∘g) (1) =g ( x ) = 4 x - 3 , h ( x ) = 3 \sqrt { x - 7 } , ( h \circ g ) ( 1 ) =g(x) =4x−3,h(x) =3x−7​,(h∘g) (1) = ?

Find the indicated function and write its domain in interval notation. - n(x) =x+3,q(x) =1x+6,(q∘n) (x) =?n ( x ) = x + 3 , q ( x ) = \frac { 1 } { x + 6 } , ( q \circ n ) ( x ) = ?n(x) =x+3,q(x) =x+61​,(q∘n) (x) =?

The graph of y = f (x) is given. Graph the indicated function. -Graph y=−f(x−2) −2y = - f ( x - 2 ) - 2y=−f(x−2) −2

Choose the one alternative that best completes the statement or answers the question. -If bottled water costs $0.63 per bottle, then the cost, C (in dollars) , for b bottles is defined by C(b) = 0.63b. How many bottles of water can be purchased for $7.56?

Solve the problem. - Use the graph of y=b(x) below to graph y=b(12x) . \text { Use the graph of } y = b ( x ) \text { below to graph } y = b \left( \frac { 1 } { 2 } x \right) \text {. } Use the graph of y=b(x) below to graph y=b(21​x) .

Find the midpoint of the line segment whose endpoints are the given points. - (5.3,4.7) ( 5.3,4.7 ) (5.3,4.7) and (7.2,−9.7) ( 7.2 , - 9.7 ) (7.2,−9.7)

Determine the slope and the y-intercept of the line. - 6=−6y6 = - 6 y6=−6y

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A graph of an equation is symmetric with respect to the -axis if replacing y by -y results in an equivalent equation.

Use the graph to solve the equation and inequality. Write the solution to the inequality in interval notation. -a. 3x−3=2x−13 x - 3 = 2 x - 13x−3=2x−1 b. 3x−3>2x−13 x - 3 > 2 x - 13x−3>2x−1

Determine which of the given points are solutions to the given equation. - $2 x ^ { 2 } + y = 4$ I. $( 3 , - 14 )$ II. $( - 3,14 )$ III. $( - 3 , - 14 )$

Graph the equation with a graphing utility on the given viewing window. - $y = 3 x - 5 \text { on } [ - 10,10,1 ] \text { by } [ - 10,10,1 ]$

Graph the function. - $s ( x ) = \left\{ \begin{array} { l l } - x + 3 & \text { for } x \leq 3 \\ \sqrt { x - 3 } & \text { for } x > 3 \end{array} \right.$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An equation of a circle written in the form $x ^ { 2 } + y ^ { 2 } + A x + B y + C = 0$ = 0 is called the form of an equation of a circle.

Identify the domain and range of the relation, and determine whether the relation is a function. - $\{ ( - 9,4 ) , ( - 1,2 ) , ( 18 , - 2 ) , ( - 1 , - 4 ) \}$

Write the domain in interval notation. - $h ( c ) = \frac { 2 } { \sqrt { c + 11 } - 1 }$

Evaluate the function for the given value of x. - $g ( x ) = 4 x - 3 , h ( x ) = 3 \sqrt { x - 7 } , ( h \circ g ) ( 1 ) =$ ?

Find the indicated function and write its domain in interval notation. - $n ( x ) = x + 3 , q ( x ) = \frac { 1 } { x + 6 } , ( q \circ n ) ( x ) = ?$

The graph of y = f (x) is given. Graph the indicated function. -Graph $y = - f ( x - 2 ) - 2$

Solve the problem. - $\text { Use the graph of } y = b ( x ) \text { below to graph } y = b \left( \frac { 1 } { 2 } x \right) \text {. }$ $Solve the problem. - \text { Use the graph of } y = b ( x ) \text { below to graph } y = b \left( \frac { 1 } { 2 } x \right) \text {. } A) B) C) D)$

Find the midpoint of the line segment whose endpoints are the given points. - $( 5.3,4.7 )$ and $( 7.2 , - 9.7 )$

Determine the slope and the y-intercept of the line. - $6 = - 6 y$