Question 1

Give the domain and range of the relation.
-

Accepted Answer

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

Question 2

Determine if the function is even, odd, or neither.
-$f ( x ) = 2 x ^ { 3 } - 4 x ^ { 2 } + 3$

Accepted Answer

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

Question 3

Find the center-radius form of the equation of the circle having a diameter with endpoints $( - 5,1 )$ and $( 3,7 )$.

Accepted Answer

A)  $( x + 1 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 25$ 
B)  $( x - 3 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 100$ 
C)  $( x + 3 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 10$ 
D)  $( x - 1 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 5$ 
A)  $( x + 1 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 25$ 
B)  $( x - 3 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 100$ 
C)  $( x + 3 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 10$ 
D)  $( x - 1 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 5$

Question 4

For the points P and Q, find the coordinates of the midpoint of the segment PQ.
-$\mathrm { P } ( - \sqrt { 10 } , 1 ) , \mathrm { Q } ( 0 , \sqrt { 5 } )$

Accepted Answer

A)  $\left( \frac { - \sqrt { 10 } + \sqrt { 5 } } { 2 } , \frac { 1 } { 2 } \right)$ 
B)  $\left( - \frac { \sqrt { 10 } } { 2 } , \frac { 1 + \sqrt { 5 } } { 2 } \right)$ 
C)  $( - \sqrt { 10 } , 1 + \sqrt { 5 } )$ 
D)  $\left( \frac { \sqrt { 10 } } { 2 } , \frac { 1 - \sqrt { 5 } } { 2 } \right)$ 
A)  $\left( \frac { - \sqrt { 10 } + \sqrt { 5 } } { 2 } , \frac { 1 } { 2 } \right)$ 
B)  $\left( - \frac { \sqrt { 10 } } { 2 } , \frac { 1 + \sqrt { 5 } } { 2 } \right)$ 
C)  $( - \sqrt { 10 } , 1 + \sqrt { 5 } )$ 
D)  $\left( \frac { \sqrt { 10 } } { 2 } , \frac { 1 - \sqrt { 5 } } { 2 } \right)$

Question 5

Give the domain and range of the relation.
-Find $f ( k )$ when $f ( x ) = 3 x ^ { 2 } + 4 x + 5$

Accepted Answer

A)  $9 k ^ { 2 } + 16 k + 25$ 
B)  $3 k ^ { 2 } + 4 k + 5$ 
C)  $3 k ^ { 2 } + 16 k + 5$ 
D)  $3 \mathrm { k } ^ { 2 } + 4 \mathrm { k } + 25$ 
A)  $9 k ^ { 2 } + 16 k + 25$ 
B)  $3 k ^ { 2 } + 4 k + 5$ 
C)  $3 k ^ { 2 } + 16 k + 5$ 
D)  $3 \mathrm { k } ^ { 2 } + 4 \mathrm { k } + 25$

Question 6

For the given functions f and g , find the indicated composition.
-$$f ( x ) = 7 x + 12 , \quad g ( x ) = 3 x - 1$$
$( f a g ) ( x )$

Accepted Answer

A)  $21 x + 5$ 
B)  $21 x + 35$ 
C)  $21 x + 11$ 
D)  $21 x + 19$ 
A)  $21 x + 5$ 
B)  $21 x + 35$ 
C)  $21 x + 11$ 
D)  $21 x + 19$

Question 7

Determine whether the three points are collinear.
-$( 13 , - 10 ) , ( 5 , - 4 ) , ( 7 , - 2 )$

Accepted Answer

A) True 
 B)False

Question 8

The graph of a linear function f is shown. Write the equation that defines f. Write the equation in slope-intercept form.
-

Accepted Answer

A)  $y = 2 x + 5$ 
B)  $y = 2 x - 5$ 
C)  $y = - 2 x + 5$ 
D)  $y = - 2 x - 5$ 
A)  $y = 2 x + 5$ 
B)  $y = 2 x - 5$ 
C)  $y = - 2 x + 5$ 
D)  $y = - 2 x - 5$

Question 9

Provide an appropriate response.
-Are the points A(-3, 5), B(0, 6), C(2, -2), and D(5, 1) the vertices of a parallelogram (opposite sides equal in length)? of a rhombus (all sides equal in length)?

Accepted Answer

A)  no; no 
B)  yes; no 
C)  yes; yes 
D)  no; yes 
A)  no; no 
B)  yes; no 
C)  yes; yes 
D)  no; yes

Question 10

Write an equation for the line described. Write the equation in the form specified.
-perpendicular to $- 2 x + y = 8$, through $( 5,4 )$; slope-intercept form

Accepted Answer

A)  $y = - \frac { 1 } { 2 } x - \frac { 13 } { 2 }$ 
B)  $y = \frac { 1 } { 2 } x - \frac { 13 } { 2 }$ 
C)  $y = - 2 x - 13$ 
D)  $y = - \frac { 1 } { 2 } x + \frac { 13 } { 2 }$ 
A)  $y = - \frac { 1 } { 2 } x - \frac { 13 } { 2 }$ 
B)  $y = \frac { 1 } { 2 } x - \frac { 13 } { 2 }$ 
C)  $y = - 2 x - 13$ 
D)  $y = - \frac { 1 } { 2 } x + \frac { 13 } { 2 }$

Question 11

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ .
-$f(x)=x^{3}-2$

Accepted Answer

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

Question 12

Match the description with the correct symbolic expression.
-a linear function whose graph passes through the origin

Accepted Answer

A)  $f ( x ) = 2$ 
B)  $x = 2$ 
C)  $6 x - 6 y = 6$ 
D)  $y = - 2 x$ 
A)  $f ( x ) = 2$ 
B)  $x = 2$ 
C)  $6 x - 6 y = 6$ 
D)  $y = - 2 x$

Question 13

Write an equation for the line described. Write the equation in the form specified.
-perpendicular to $2 x - 5 y = - 19$, through $( 3 , - 5 )$; slope-intercept form

Accepted Answer

A)  $y = - \frac { 3 } { 5 } x - \frac { 19 } { 5 }$ 
B)  $y = - \frac { 5 } { 2 } x + \frac { 5 } { 2 }$ 
C)  $y = - \frac { 2 } { 5 } x - \frac { 2 } { 5 }$ 
D)  $y = \frac { 5 } { 2 } x + \frac { 5 } { 2 }$ 
A)  $y = - \frac { 3 } { 5 } x - \frac { 19 } { 5 }$ 
B)  $y = - \frac { 5 } { 2 } x + \frac { 5 } { 2 }$ 
C)  $y = - \frac { 2 } { 5 } x - \frac { 2 } { 5 }$ 
D)  $y = \frac { 5 } { 2 } x + \frac { 5 } { 2 }$

Question 14

For the points P and Q, find the coordinates of the midpoint of the segment PQ.
-$\mathrm { P } ( 7 \sqrt { 3 } , - \sqrt { 13 } ) , \mathrm { Q } ( - \sqrt { 3 } , 0 )$

Accepted Answer

A)  $\left( 3 \sqrt { 3 } , - \frac { \sqrt { 13 } } { 2 } \right)$ 
B)  $( - 3,13 )$ 
C)  $\left( 3 \sqrt { 6 } , - \frac { \sqrt { 39 } } { 2 } \right)$ 
D)  $\left( 4 \sqrt { 3 } , \frac { \sqrt { 13 } } { 2 } \right)$ 
A)  $\left( 3 \sqrt { 3 } , - \frac { \sqrt { 13 } } { 2 } \right)$ 
B)  $( - 3,13 )$ 
C)  $\left( 3 \sqrt { 6 } , - \frac { \sqrt { 39 } } { 2 } \right)$ 
D)  $\left( 4 \sqrt { 3 } , \frac { \sqrt { 13 } } { 2 } \right)$

Question 15

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

Accepted Answer

A)  It is the graph of $f ( x ) = | x |$ translated 3 units to the right and 7 units down. The equation is $y = | x + 3 | - 7$ 
B)  It is the graph of $\mathrm { f } ( \mathrm { x } ) = | \mathrm { x } |$ translated 3 units to the right and 7 units down. The equation is $y = | x - 3 | - 7$ 
C)  It is the graph of $f ( x ) = | x |$ translated 3 units to the right and 7 units down. The equation is $y = | x - 3 | + 7$ 
D)  It is the graph of $f ( x ) = | x |$ translated 3 units to the right and 7 units down. The equation is $y = | x + 3 | + 7$ 
A)  It is the graph of $f ( x ) = | x |$ translated 3 units to the right and 7 units down. The equation is $y = | x + 3 | - 7$ 
B)  It is the graph of $\mathrm { f } ( \mathrm { x } ) = | \mathrm { x } |$ translated 3 units to the right and 7 units down. The equation is $y = | x - 3 | - 7$ 
C)  It is the graph of $f ( x ) = | x |$ translated 3 units to the right and 7 units down. The equation is $y = | x - 3 | + 7$ 
D)  It is the graph of $f ( x ) = | x |$ translated 3 units to the right and 7 units down. The equation is $y = | x + 3 | + 7$

Question 16

Give the domain and range of the relation.
-

Accepted Answer

A)  domain: $( - \infty , \infty )$; range: $( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
B)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
C)  domain: $\{ - 2 \}$; range: $( - \infty , \infty )$ 
D)  domain: $( - \infty , \infty )$; range: $\{ - 2 \}$ 
A)  domain: $( - \infty , \infty )$; range: $( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
B)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
C)  domain: $\{ - 2 \}$; range: $( - \infty , \infty )$ 
D)  domain: $( - \infty , \infty )$; range: $\{ - 2 \}$

Question 17

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

Accepted Answer

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

Question 18

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.
-$$y = - 0.66 x ^ { 4 } + x ^ { 2 } + 6$$

Accepted Answer

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

Question 19

The table lists the average composite scores on a national entrance exam for selected years. $$\begin{array} { c | c c c c c c c } 
\text { Year } & 2 & 4 & 6 & 8 & 10 & 12 & 14 \
\hline \text { Score } & 122.7 & 131.5 & 131.5 & 129.5 & 133.9 & 132.0 & 130.0
\end{array}$$ (i) Make a line graph of the data. (ii) If the graph represents a piecewise-linear function f, find a symbolic representation for the piece of f located on
The interval [4, 6].

Accepted Answer

A)  $$f ( x ) = 4.4 x - 8589.3 \text { if } 8 \leq x \leq 10$$
  
B)  $$f ( x ) = 131.5 \text { if } 4 \leq x \leq 6$$
  
C)  none of these 
D)  $$f ( x ) = 0.75 x - 1355 \text { if } 4 \leq x \leq 8$$
  
A)  $$f ( x ) = 4.4 x - 8589.3 \text { if } 8 \leq x \leq 10$$
  
B)  $$f ( x ) = 131.5 \text { if } 4 \leq x \leq 6$$
  
C)  none of these 
D)  $$f ( x ) = 0.75 x - 1355 \text { if } 4 \leq x \leq 8$$

Question 20

Use the graphs to find the value of $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( 3 )$.

Accepted Answer

A)  1 
B)  undefined 
C)  $- 2$ 
D)  $- 1$ 
A)  1 
B)  undefined 
C)  $- 2$ 
D)  $- 1$

Give the domain and range of the relation. -

Determine if the function is even, odd, or neither. - $f ( x ) = 2 x ^ { 3 } - 4 x ^ { 2 } + 3$

Find the center-radius form of the equation of the circle having a diameter with endpoints $( - 5,1 )$ and $( 3,7 )$ .

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $\mathrm { P } ( - \sqrt { 10 } , 1 ) , \mathrm { Q } ( 0 , \sqrt { 5 } )$

Give the domain and range of the relation. -Find $f ( k )$ when $f ( x ) = 3 x ^ { 2 } + 4 x + 5$

For the given functions f and g , find the indicated composition. - $f ( x ) = 7 x + 12 , \quad g ( x ) = 3 x - 1$ $( f a g ) ( x )$

Determine whether the three points are collinear. - $( 13 , - 10 ) , ( 5 , - 4 ) , ( 7 , - 2 )$

The graph of a linear function f is shown. Write the equation that defines f. Write the equation in slope-intercept form. -

Provide an appropriate response. -Are the points A(-3, 5), B(0, 6), C(2, -2), and D(5, 1) the vertices of a parallelogram (opposite sides equal in length)? of a rhombus (all sides equal in length)?

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $- 2 x + y = 8$ , through $( 5,4 )$ ; slope-intercept form

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ . - $f(x)=x^{3}-2$ $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } . - f(x)=x^{3}-2$

Match the description with the correct symbolic expression. -a linear function whose graph passes through the origin

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $2 x - 5 y = - 19$ , through $( 3 , - 5 )$ ; slope-intercept form

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $\mathrm { P } ( 7 \sqrt { 3 } , - \sqrt { 13 } ) , \mathrm { Q } ( - \sqrt { 3 } , 0 )$

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

Give the domain and range of the relation. -

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 whether the equation has a graph that is symmetric with respect to the y-axis, the x-axis, the origin, or none of these. - $y = - 0.66 x ^ { 4 } + x ^ { 2 } + 6$

Use the graphs to find the value of $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( 3 )$ . $Use the graphs to find the value of \left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( 3 ) .$

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. -

Determine if the function is even, odd, or neither. - f(x)=2x3−4x2+3f ( x ) = 2 x ^ { 3 } - 4 x ^ { 2 } + 3f(x)=2x3−4x2+3

Find the center-radius form of the equation of the circle having a diameter with endpoints (−5,1)( - 5,1 )(−5,1) and (3,7)( 3,7 )(3,7) .

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - P(−10,1),Q(0,5)\mathrm { P } ( - \sqrt { 10 } , 1 ) , \mathrm { Q } ( 0 , \sqrt { 5 } )P(−10​,1),Q(0,5​)

Give the domain and range of the relation. -Find f(k)f ( k )f(k) when f(x)=3x2+4x+5f ( x ) = 3 x ^ { 2 } + 4 x + 5f(x)=3x2+4x+5

For the given functions f and g , find the indicated composition. - f(x)=7x+12,g(x)=3x−1f ( x ) = 7 x + 12 , \quad g ( x ) = 3 x - 1f(x)=7x+12,g(x)=3x−1 (fag)(x)( f a g ) ( x )(fag)(x)

Determine whether the three points are collinear. - (13,−10),(5,−4),(7,−2)( 13 , - 10 ) , ( 5 , - 4 ) , ( 7 , - 2 )(13,−10),(5,−4),(7,−2)

The graph of a linear function f is shown. Write the equation that defines f. Write the equation in slope-intercept form. -

Provide an appropriate response. -Are the points A(-3, 5), B(0, 6), C(2, -2), and D(5, 1) the vertices of a parallelogram (opposite sides equal in length)? of a rhombus (all sides equal in length)?

Write an equation for the line described. Write the equation in the form specified. -perpendicular to −2x+y=8- 2 x + y = 8−2x+y=8 , through (5,4)( 5,4 )(5,4) ; slope-intercept form

Describe how the graph of the equation relates to the graph of y y=x3y = \sqrt [ 3 ] { x }y=3x​ . - f(x)=x3−2f(x)=x^{3}-2f(x)=x3−2

Match the description with the correct symbolic expression. -a linear function whose graph passes through the origin

Write an equation for the line described. Write the equation in the form specified. -perpendicular to 2x−5y=−192 x - 5 y = - 192x−5y=−19 , through (3,−5)( 3 , - 5 )(3,−5) ; slope-intercept form

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - P(73,−13),Q(−3,0)\mathrm { P } ( 7 \sqrt { 3 } , - \sqrt { 13 } ) , \mathrm { Q } ( - \sqrt { 3 } , 0 )P(73​,−13​),Q(−3​,0)

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

Give the domain and range of the relation. -

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

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=−0.66x4+x2+6y = - 0.66 x ^ { 4 } + x ^ { 2 } + 6y=−0.66x4+x2+6

Use the graphs to find the value of (fg)(3)\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( 3 )(gf​)(3) .

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

Determine if the function is even, odd, or neither. - $f ( x ) = 2 x ^ { 3 } - 4 x ^ { 2 } + 3$

Find the center-radius form of the equation of the circle having a diameter with endpoints $( - 5,1 )$ and $( 3,7 )$ .

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $\mathrm { P } ( - \sqrt { 10 } , 1 ) , \mathrm { Q } ( 0 , \sqrt { 5 } )$

Give the domain and range of the relation. -Find $f ( k )$ when $f ( x ) = 3 x ^ { 2 } + 4 x + 5$

For the given functions f and g , find the indicated composition. - $f ( x ) = 7 x + 12 , \quad g ( x ) = 3 x - 1$ $( f a g ) ( x )$

Determine whether the three points are collinear. - $( 13 , - 10 ) , ( 5 , - 4 ) , ( 7 , - 2 )$

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $- 2 x + y = 8$ , through $( 5,4 )$ ; slope-intercept form

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ . - $f(x)=x^{3}-2$ $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } . - f(x)=x^{3}-2$

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $2 x - 5 y = - 19$ , through $( 3 , - 5 )$ ; slope-intercept form

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $\mathrm { P } ( 7 \sqrt { 3 } , - \sqrt { 13 } ) , \mathrm { Q } ( - \sqrt { 3 } , 0 )$

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 whether the equation has a graph that is symmetric with respect to the y-axis, the x-axis, the origin, or none of these. - $y = - 0.66 x ^ { 4 } + x ^ { 2 } + 6$

Use the graphs to find the value of $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( 3 )$ . $Use the graphs to find the value of \left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( 3 ) .$