Question 1

Evaluate as indicated.
-If $f ( x ) = 4 x ^ { 2 } + 4 x - 5$, find and simplify $f ( 2 + x )$.

Accepted Answer

A)  $4 x ^ { 2 } + 4 x - 7$ 
B)  $4 x ^ { 2 } + 20 x + 19$ 
C)  $19 + x$ 
D)  $4 x ^ { 2 } + 2 x + 19$ 
A)  $4 x ^ { 2 } + 4 x - 7$ 
B)  $4 x ^ { 2 } + 20 x + 19$ 
C)  $19 + x$ 
D)  $4 x ^ { 2 } + 2 x + 19$

Question 2

Compute the least-squares regression line for the given data set.
-$\begin{array}{c|cccccc}
x & 2 & 3 & 4 & 5 & 6 & 7 \
\hline y & 3.4 & -1.7 & -3 & -4.3 & -10.9 & -13.9
\end{array}$

Accepted Answer

A)  $y = 3.46 x + 3.4$ 
B)  $y = 9.77 x - 3.30$ 
C)  $y = - 3.30 x + 9.77$ 
D)  $y = 3.46 x + 9.77$ 
A)  $y = 3.46 x + 3.4$ 
B)  $y = 9.77 x - 3.30$ 
C)  $y = - 3.30 x + 9.77$ 
D)  $y = 3.46 x + 9.77$

Question 3

Determine whether the relation defines y as a function of x.
-$( x + 6 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 25$

Accepted Answer

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

Question 4

For the given relation, write the domain, write the range, and determine if the relation defines y as a
function of x.
-

Accepted Answer

A)  Domain: $\{ - 4 , - 2,4 \}$; Range: $\{ - 1,1,3 \}$; function 
B)  Domain: $\{ - 4 , - 2,4 \}$; Range: $\{ - 1,1,3 \}$; not a function 
C)  Domain: $\{ - 1,1,3 \}$; Range: $\{ - 4 , - 2,4 \}$; function 
D)  Domain: $\{ - 1,1,3 \}$; Range: $\{ - 4 , - 2,4 \}$; not a function 
A)  Domain: $\{ - 4 , - 2,4 \}$; Range: $\{ - 1,1,3 \}$; function 
B)  Domain: $\{ - 4 , - 2,4 \}$; Range: $\{ - 1,1,3 \}$; not a function 
C)  Domain: $\{ - 1,1,3 \}$; Range: $\{ - 4 , - 2,4 \}$; function 
D)  Domain: $\{ - 1,1,3 \}$; Range: $\{ - 4 , - 2,4 \}$; not a function

Question 5

Evaluate the function for the given values of x.
-$f ( x ) = \left\{ \begin{array} { l l } - 5 x + 4 , & \text { for } x < - 1 \ x ^ { 2 } + 3 , & \text { for } - 1 \leq x < 2 \ 1 , & \text { for } x \geq 2 \end{array} \right.$
(a) $f ( - 1 )$; (b) $f ( 3 )$

Accepted Answer

A)  (a) 9; (b) 12 
B)  (a) 4 ;
(b) 12 
C)  (a) $4 ;$ (b) 1 
D)  (a) $9 ;$ (b) 1 
A)  (a) 9; (b) 12 
B)  (a) 4 ;
(b) 12 
C)  (a) $4 ;$ (b) 1 
D)  (a) $9 ;$ (b) 1

Question 6

Determine if the lines defined by the given equations are parallel, perpendicular, or neither.
-$$\begin{array} { l } 
- 4 x - 9 y = - 4 \
\frac { 2 } { 3 } x + \frac { 3 } { 2 } y = - 9
\end{array}$$

Accepted Answer

A)  parallel 
B)  neither 
C)  perpendicular 
A)  parallel 
B)  neither 
C)  perpendicular

Question 7

Use transformations to graph the given function.
-$$f ( x ) = 3 x ^ { 2 }$$

Accepted Answer

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

Question 8

Use translations to graph the given function.
-$$a ( x ) = \sqrt { x - 2 } - 1$$

Accepted Answer

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

Question 9

Sketch the graph using transformations of a parent function (without a table of values).
-$$m ( x ) = \frac { 1 } { x } + 3$$

Accepted Answer

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

Question 10

Graph the function.
-$m ( x ) = \left\{ \begin{array} { l l } 5 & \text { for } - 4 < x < - 2 \ - x & \text { for } - 2 \leq x < 3 \ \sqrt { x - 3 } & \text { for } x \geq 3 \end{array} \right.$

Accepted Answer

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

Question 11

Solve the problem.
-If $x$ is twice $y$, and $z$ is two less than $x$, write $z$ as a function of $y$.

Accepted Answer

A)  $\mathrm { z } ( y ) = 2 y - 2$ 
B)  $z ( y ) = 2 - 2 y$ 
C)  $\mathrm { z } ( y ) = 2 ( y - 2 )$ 
D)  $\mathrm { z } ( y ) = 2 ( 2 - y )$ 
A)  $\mathrm { z } ( y ) = 2 y - 2$ 
B)  $z ( y ) = 2 - 2 y$ 
C)  $\mathrm { z } ( y ) = 2 ( y - 2 )$ 
D)  $\mathrm { z } ( y ) = 2 ( 2 - y )$

Question 12

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius.
-$$x ^ { 2 } + y ^ { 2 } + 22 x + 21 = 0$$

Accepted Answer

A)  $( x + 22 ) ^ { 2 } + y ^ { 2 } = 21$
Center: $( - 22,0 ) ; r = 21$ 
B)  $( x + 22 ) ^ { 2 } + y ^ { 2 } = 21$
Center: $( 0,22 ) ; r = 21$ 
C)  $( x + 11 ) ^ { 2 } + y ^ { 2 } = 100$
Center: $( - 11,0 ) ; r = 10$ 
D)  $( x + 11 ) ^ { 2 } + y ^ { 2 } = 100$
Center: $( 0,11 ) ; r = 10$ 
A)  $( x + 22 ) ^ { 2 } + y ^ { 2 } = 21$
Center: $( - 22,0 ) ; r = 21$ 
B)  $( x + 22 ) ^ { 2 } + y ^ { 2 } = 21$
Center: $( 0,22 ) ; r = 21$ 
C)  $( x + 11 ) ^ { 2 } + y ^ { 2 } = 100$
Center: $( - 11,0 ) ; r = 10$ 
D)  $( x + 11 ) ^ { 2 } + y ^ { 2 } = 100$
Center: $( 0,11 ) ; r = 10$

Question 13

Find an equation of the circle with the given characteristics.
-Center $( - 10 , - 2 )$ and radius 6

Accepted Answer

A)  $( x - 10 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 6$ 
B)  $( x + 10 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 6$ 
C)  $( x + 10 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 36$ 
D)  $( x - 10 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 36$ 
A)  $( x - 10 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 6$ 
B)  $( x + 10 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 6$ 
C)  $( x + 10 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 36$ 
D)  $( x - 10 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 36$

Question 14

Determine the slope of the line passing through the given points.
-$\left( \frac { 3 } { 5 } , \frac { 2 } { 3 } \right)$ and $\left( - \frac { 1 } { 9 } , - \frac { 8 } { 7 } \right)$

Accepted Answer

A)  $m = \frac { 285 } { 112 }$ 
B)  $m = - \frac { 75 } { 77 }$ 
C)  $m = - \frac { 285 } { 77 }$ 
D)  $m = - \frac { 21 } { 325 }$ 
A)  $m = \frac { 285 } { 112 }$ 
B)  $m = - \frac { 75 } { 77 }$ 
C)  $m = - \frac { 285 } { 77 }$ 
D)  $m = - \frac { 21 } { 325 }$

Question 15

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-A diagram is a visual representation of a set of data points represented as ordered
pairs.

Accepted Answer

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

Question 16

Choose the one alternative that best completes the statement or answers the question.
Graph the equation and identify the x- and y-intercepts.
-$$- 5 x - 2 y = 10$$

Accepted Answer

A)  $x$-intercept: $( - 5,0 )$;
$y$-intercept: $( 0,2 )$
  
B)  $x$-intercept: $( 2,0 )$;
$y$-intercept: $( 0 , - 5 )$
  
C)  $x$-intercept: $( - 2,0 )$;
$y$-intercept: $( 0 , - 5 )$
  
D)  $x$-intercept: $( - 5,0 )$;
$y$-intercept: $( 0 , - 2 )$
  
A)  $x$-intercept: $( - 5,0 )$;
$y$-intercept: $( 0,2 )$
  
B)  $x$-intercept: $( 2,0 )$;
$y$-intercept: $( 0 , - 5 )$
  
C)  $x$-intercept: $( - 2,0 )$;
$y$-intercept: $( 0 , - 5 )$
  
D)  $x$-intercept: $( - 5,0 )$;
$y$-intercept: $( 0 , - 2 )$

Question 17

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The slope between any two distinct points on a nonvertical line is a constant.

Accepted Answer

A) True 
 B)False

Question 18

Write the domain in interval notation.
-$$r ( x ) = \frac { - 14 } { x ^ { 2 } + 81 }$$

Accepted Answer

A)  $( \infty , 0 ) \cup ( 0 , \infty )$ 
B)  $( \infty , \infty )$ 
C)  $( \infty , - 9 ) \cup ( 9 , \infty )$ 
D)  $( - \infty , - 9 ) \cup ( - 9,9 ) \cup ( 9 , \infty )$ 
A)  $( \infty , 0 ) \cup ( 0 , \infty )$ 
B)  $( \infty , \infty )$ 
C)  $( \infty , - 9 ) \cup ( 9 , \infty )$ 
D)  $( - \infty , - 9 ) \cup ( - 9,9 ) \cup ( 9 , \infty )$

Question 19

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius.
-$$x ^ { 2 } + y ^ { 2 } + 16 x + 8 y - 20 = 0$$

Accepted Answer

A)  $( x + 16 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 20$
Center: $( 16,8 ) ; r = 20$ 
B)  $( x + 16 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 20$
Center: $( - 16 , - 8 ) ; r = 20$ 
C)  $( x + 8 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 100$
Center: $( - 8 , - 4 ) ; r = 10$ 
D)  $( x + 8 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 100$
Center: $( 8,4 ) ; r = 10$ 
A)  $( x + 16 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 20$
Center: $( 16,8 ) ; r = 20$ 
B)  $( x + 16 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 20$
Center: $( - 16 , - 8 ) ; r = 20$ 
C)  $( x + 8 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 100$
Center: $( - 8 , - 4 ) ; r = 10$ 
D)  $( x + 8 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 100$
Center: $( 8,4 ) ; r = 10$

Question 20

Solve the problem.
-A map of a hiking area is drawn so that the Visitor Center is at the origin of a rectangular grid. Two hikers are located at positions $( - 2,1 )$ and $( 1 , - 3 )$ with respect to the Visitor Center where all units are miles. A campground is located exactly halfway between the hikers. What are the coordinates of the campground?

Accepted Answer

A)  $\left( - \frac { 1 } { 2 } , 2 \right)$ 
B)  $\left( - \frac { 1 } { 2 } , - 1 \right)$ 
C)  $\left( - \frac { 3 } { 2 } , - 1 \right)$ 
D)  $\left( - \frac { 3 } { 2 } , 2 \right)$ 
A)  $\left( - \frac { 1 } { 2 } , 2 \right)$ 
B)  $\left( - \frac { 1 } { 2 } , - 1 \right)$ 
C)  $\left( - \frac { 3 } { 2 } , - 1 \right)$ 
D)  $\left( - \frac { 3 } { 2 } , 2 \right)$

Evaluate as indicated. -If $f ( x ) = 4 x ^ { 2 } + 4 x - 5$ , find and simplify $f ( 2 + x )$ .

Compute the least-squares regression line for the given data set. - x 2 3 4 5 6 7 y 3.4 -1.7 -3 -4.3 -10.9 -13.9

Determine whether the relation defines y as a function of x. - $( x + 6 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 25$

For the given relation, write the domain, write the range, and determine if the relation defines y as a function of x. -

Evaluate the function for the given values of x. - $f ( x ) = \left\{ \begin{array} { l l } - 5 x + 4 , & \text { for } x < - 1 \\ x ^ { 2 } + 3 , & \text { for } - 1 \leq x < 2 \\ 1 , & \text { for } x \geq 2 \end{array} \right.$ (a) $f ( - 1 )$ ; (b) $f ( 3 )$

Determine if the lines defined by the given equations are parallel, perpendicular, or neither. - -4x-9y=-4 x+y=-9

Use transformations to graph the given function. - $f ( x ) = 3 x ^ { 2 }$

Use translations to graph the given function. - $a ( x ) = \sqrt { x - 2 } - 1$

Sketch the graph using transformations of a parent function (without a table of values). - $m ( x ) = \frac { 1 } { x } + 3$

Graph the function. - $m ( x ) = \left\{ \begin{array} { l l } 5 & \text { for } - 4 < x < - 2 \\ - x & \text { for } - 2 \leq x < 3 \\ \sqrt { x - 3 } & \text { for } x \geq 3 \end{array} \right.$

Solve the problem. -If $x$ is twice $y$ , and $z$ is two less than $x$ , write $z$ as a function of $y$ .

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $x ^ { 2 } + y ^ { 2 } + 22 x + 21 = 0$

Find an equation of the circle with the given characteristics. -Center $( - 10 , - 2 )$ and radius 6

Determine the slope of the line passing through the given points. - $\left( \frac { 3 } { 5 } , \frac { 2 } { 3 } \right)$ and $\left( - \frac { 1 } { 9 } , - \frac { 8 } { 7 } \right)$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A diagram is a visual representation of a set of data points represented as ordered pairs.

Choose the one alternative that best completes the statement or answers the question. Graph the equation and identify the x- and y-intercepts. - $- 5 x - 2 y = 10$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The slope between any two distinct points on a nonvertical line is a constant.

Write the domain in interval notation. - $r ( x ) = \frac { - 14 } { x ^ { 2 } + 81 }$

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $x ^ { 2 } + y ^ { 2 } + 16 x + 8 y - 20 = 0$

Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Exam 2: Functions and Relations

Evaluate as indicated. -If f(x)=4x2+4x−5f ( x ) = 4 x ^ { 2 } + 4 x - 5f(x)=4x2+4x−5 , find and simplify f(2+x)f ( 2 + x )f(2+x) .

Compute the least-squares regression line for the given data set. - x 2 3 4 5 6 7 y 3.4 -1.7 -3 -4.3 -10.9 -13.9

Determine whether the relation defines y as a function of x. - (x+6)2+(y−7)2=25( x + 6 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 25(x+6)2+(y−7)2=25

For the given relation, write the domain, write the range, and determine if the relation defines y as a function of x. -

Determine if the lines defined by the given equations are parallel, perpendicular, or neither. - -4x-9y=-4 x+y=-9

Use transformations to graph the given function. - f(x)=3x2f ( x ) = 3 x ^ { 2 }f(x)=3x2

Use translations to graph the given function. - a(x)=x−2−1a ( x ) = \sqrt { x - 2 } - 1a(x)=x−2​−1

Sketch the graph using transformations of a parent function (without a table of values). - m(x)=1x+3m ( x ) = \frac { 1 } { x } + 3m(x)=x1​+3

Solve the problem. -If xxx is twice yyy , and zzz is two less than xxx , write zzz as a function of yyy .

Write the given equation in the form (x−h)2+(y−k)2=r2( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }(x−h)2+(y−k)2=r2 . Identify the center and radius. - x2+y2+22x+21=0x ^ { 2 } + y ^ { 2 } + 22 x + 21 = 0x2+y2+22x+21=0

Find an equation of the circle with the given characteristics. -Center (−10,−2)( - 10 , - 2 )(−10,−2) and radius 6

Determine the slope of the line passing through the given points. - (35,23)\left( \frac { 3 } { 5 } , \frac { 2 } { 3 } \right)(53​,32​) and (−19,−87)\left( - \frac { 1 } { 9 } , - \frac { 8 } { 7 } \right)(−91​,−78​)

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A diagram is a visual representation of a set of data points represented as ordered pairs.

Choose the one alternative that best completes the statement or answers the question. Graph the equation and identify the x- and y-intercepts. - −5x−2y=10- 5 x - 2 y = 10−5x−2y=10

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The slope between any two distinct points on a nonvertical line is a constant.

Write the domain in interval notation. - r(x)=−14x2+81r ( x ) = \frac { - 14 } { x ^ { 2 } + 81 }r(x)=x2+81−14​

Write the given equation in the form (x−h)2+(y−k)2=r2( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }(x−h)2+(y−k)2=r2 . Identify the center and radius. - x2+y2+16x+8y−20=0x ^ { 2 } + y ^ { 2 } + 16 x + 8 y - 20 = 0x2+y2+16x+8y−20=0

Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Evaluate as indicated. -If $f ( x ) = 4 x ^ { 2 } + 4 x - 5$ , find and simplify $f ( 2 + x )$ .

Determine whether the relation defines y as a function of x. - $( x + 6 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 25$

Use transformations to graph the given function. - $f ( x ) = 3 x ^ { 2 }$

Use translations to graph the given function. - $a ( x ) = \sqrt { x - 2 } - 1$

Sketch the graph using transformations of a parent function (without a table of values). - $m ( x ) = \frac { 1 } { x } + 3$

Solve the problem. -If $x$ is twice $y$ , and $z$ is two less than $x$ , write $z$ as a function of $y$ .

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $x ^ { 2 } + y ^ { 2 } + 22 x + 21 = 0$

Find an equation of the circle with the given characteristics. -Center $( - 10 , - 2 )$ and radius 6

Determine the slope of the line passing through the given points. - $\left( \frac { 3 } { 5 } , \frac { 2 } { 3 } \right)$ and $\left( - \frac { 1 } { 9 } , - \frac { 8 } { 7 } \right)$

Choose the one alternative that best completes the statement or answers the question. Graph the equation and identify the x- and y-intercepts. - $- 5 x - 2 y = 10$

Write the domain in interval notation. - $r ( x ) = \frac { - 14 } { x ^ { 2 } + 81 }$

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $x ^ { 2 } + y ^ { 2 } + 16 x + 8 y - 20 = 0$