Question 1

Evaluate the function.
-Find $f ( k )$ when $f ( x ) = 3 x ^ { 2 } + 4 x + 5$

Accepted Answer

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

Question 2

Graph the function.
-$f(x)=\left\{\begin{array}{ll}
x^{2}-9, & \text { if } x1
\end{array}\right.$

Accepted Answer

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

Question 3

Find the specified domain.
-Find the domain of $( f g ) ( x )$ when $f ( x ) = \sqrt { 5 x + 4 }$ and $g ( x ) = \sqrt { 5 x - 6 }$

Accepted Answer

A)  $[ 0 , \infty )$ 
B)  $\left[ - \frac { 6 } { 5 } , \infty \right)$ 
C)  $\left[ \frac { 6 } { 5 } , \infty \right)$ 
D)  $( - \infty , \infty )$ 
A)  $[ 0 , \infty )$ 
B)  $\left[ - \frac { 6 } { 5 } , \infty \right)$ 
C)  $\left[ \frac { 6 } { 5 } , \infty \right)$ 
D)  $( - \infty , \infty )$

Question 4

Evaluate the function.
-Find $g ( a - 1 )$ when $g ( x ) = 5 x + 2$

Accepted Answer

A)  $5 a + 1$ 
B)  $\frac { 1 } { 5 } a + 2$ 
C)  $5 a - 3$ 
D)  $5 a + 2$ 
A)  $5 a + 1$ 
B)  $\frac { 1 } { 5 } a + 2$ 
C)  $5 a - 3$ 
D)  $5 a + 2$

Question 5

Use a graphing calculator to solve the linear equation.
-$$( - 8 x - 2 ) - 7 = - 7 ( x + 7 )$$

Accepted Answer

A)  $\{ 16 \}$ 
B)  $\{ 40 \}$ 
C)  $\{ - 54 \}$ 
D)  $\{ - 40 \}$ 
A)  $\{ 16 \}$ 
B)  $\{ 40 \}$ 
C)  $\{ - 54 \}$ 
D)  $\{ - 40 \}$

Question 6

Give the domain and range of the relation.
-

Accepted Answer

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

Question 7

Refer to the following graphs to determine an appropriate response.  
-Which one is discontinuous over its domain? What is its range?

Accepted Answer

A)  graph $C ; \{ - 2 , - 1,0,1,2 \}$ 
B)  graph $C ; ( - \infty , \infty )$ 
C)  graph $B ; ( - \infty , \infty )$ 
D)  graph $B ; [ 0 , \infty )$ 
A)  graph $C ; \{ - 2 , - 1,0,1,2 \}$ 
B)  graph $C ; ( - \infty , \infty )$ 
C)  graph $B ; ( - \infty , \infty )$ 
D)  graph $B ; [ 0 , \infty )$

Question 8

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-midpoint (-6, 0), endpoint (-5, -5)

Accepted Answer

A)  (-7, 5) 
B)  (5, -7) 
C)  (-3, -15) 
D)  (-7, -10) 
A)  (-7, 5) 
B)  (5, -7) 
C)  (-3, -15) 
D)  (-7, -10)

Question 9

Determine whether the three points are collinear.
-(-9, 8), (-5, -1), (0, 4)

Accepted Answer

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

Question 10

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-midpoint $\left( \frac { p + d } { 2 } , \frac { q - y } { 2 } \right)$, endpoint $( p , q )$

Accepted Answer

A)  $\left( \frac { \mathrm { d } } { 2 } , - \frac { \mathrm { y } } { 2 } \right)$ 
B)  $\left( \frac { 3 p + d } { 4 } , \frac { 3 q - y } { 4 } \right)$ 
C)  $( \mathrm { d } , \mathrm { y } )$ 
D)  $( \mathrm { d } , - \mathrm { y } )$ 
A)  $\left( \frac { \mathrm { d } } { 2 } , - \frac { \mathrm { y } } { 2 } \right)$ 
B)  $\left( \frac { 3 p + d } { 4 } , \frac { 3 q - y } { 4 } \right)$ 
C)  $( \mathrm { d } , \mathrm { y } )$ 
D)  $( \mathrm { d } , - \mathrm { y } )$

Question 11

For the points P and Q, find the coordinates of the midpoint of the segment PQ.
-$$\mathrm { P } ( 6,5 ) , \mathrm { Q } ( 9 , - 2 )$$

Accepted Answer

A)  $( - 3,7 )$ 
B)  $( 15,3 )$ 
C)  $\left( \frac { 15 } { 2 } , \frac { 3 } { 2 } \right)$ 
D)  $\left( - \frac { 3 } { 2 } , \frac { 7 } { 2 } \right)$ 
A)  $( - 3,7 )$ 
B)  $( 15,3 )$ 
C)  $\left( \frac { 15 } { 2 } , \frac { 3 } { 2 } \right)$ 
D)  $\left( - \frac { 3 } { 2 } , \frac { 7 } { 2 } \right)$

Question 12

Provide an appropriate response.
-Are the points A(-3, 11), B(0, 8), C(2, 0), and D(5, 3) the vertices of a parallelogram (opposite sides equal in length)? of a rhombus (all sides equal in length)?

Accepted Answer

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

Question 13

Write an equation for the line described. Write the equation in the form specified.
-parallel to $x = - 7$, through $( 2,5 )$

Accepted Answer

A)  $x = 2$ 
B)  $\mathrm { y } = - 7$ 
C)  $x = 5$ 
D)  $y = 5$ 
A)  $x = 2$ 
B)  $\mathrm { y } = - 7$ 
C)  $x = 5$ 
D)  $y = 5$

Question 14

Write an equation for the line described. Write the equation in the form specified.
-perpendicular to x = 6, through (3, 5)

Accepted Answer

A)  y = 3 
B) x = 3 
C) x = 5 
D) y = 5 
A)  y = 3 
B) x = 3 
C) x = 5 
D) y = 5

Question 15

Use the graph to solve the problem.
-The graph shows the relationship between current I and resistance $R$ if the voltage is fixed. Find the current if the resistance is $2.4 \Omega$.

Accepted Answer

A)  $1.8 \mathrm {~A}$ 
B)  $2.0 \mathrm {~A}$ 
C)  $2.2 \mathrm {~A}$ 
D)  $1.6 \mathrm {~A}$ 
A)  $1.8 \mathrm {~A}$ 
B)  $2.0 \mathrm {~A}$ 
C)  $2.2 \mathrm {~A}$ 
D)  $1.6 \mathrm {~A}$

Question 16

Graph the circle.
-$x^{2}+(y-1)^{2}=4$

Accepted Answer

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

Question 17

Match the description with the correct symbolic expression.
-a linear equation whose graph has x-intercept -6 and y-intercept 6

Accepted Answer

A)  x = 6 
B) -6x + 6y = 36 
C)  y = 6x + 36 
D)  f(x) = -6 
A)  x = 6 
B) -6x + 6y = 36 
C)  y = 6x + 36 
D)  f(x) = -6

Question 18

Determine the intervals of the domain over which the function is continuous.
-

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $( - \infty , 1 ) \cup ( 1 , \infty )$ 
C)  $[ 1 , \infty )$ 
D)  $[ 2 , \infty )$ 
A)  $( - \infty , \infty )$ 
B)  $( - \infty , 1 ) \cup ( 1 , \infty )$ 
C)  $[ 1 , \infty )$ 
D)  $[ 2 , \infty )$

Question 19

Write an equation for the line described. Give your answer in slope-intercept form.
-horizontal, through $( - 5 , - 3 )$

Accepted Answer

A)  $x = - 5$ 
B)  $y = - 5$ 
C)  $\mathrm { y } = - 3$ 
D)  $x = - 3$ 
A)  $x = - 5$ 
B)  $y = - 5$ 
C)  $\mathrm { y } = - 3$ 
D)  $x = - 3$

Question 20

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such.
-$f(x)=\frac{1}{4} x$

Accepted Answer

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

Evaluate the function. -Find $f ( k )$ when $f ( x ) = 3 x ^ { 2 } + 4 x + 5$

Find the specified domain. -Find the domain of $( f g ) ( x )$ when $f ( x ) = \sqrt { 5 x + 4 }$ and $g ( x ) = \sqrt { 5 x - 6 }$

Evaluate the function. -Find $g ( a - 1 )$ when $g ( x ) = 5 x + 2$

Use a graphing calculator to solve the linear equation. - $( - 8 x - 2 ) - 7 = - 7 ( x + 7 )$

Give the domain and range of the relation. -

Refer to the following graphs to determine an appropriate response. -Which one is discontinuous over its domain? What is its range?

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint (-6, 0), endpoint (-5, -5)

Determine whether the three points are collinear. -(-9, 8), (-5, -1), (0, 4)

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint $\left( \frac { p + d } { 2 } , \frac { q - y } { 2 } \right)$ , endpoint $( p , q )$

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $\mathrm { P } ( 6,5 ) , \mathrm { Q } ( 9 , - 2 )$

Provide an appropriate response. -Are the points A(-3, 11), B(0, 8), C(2, 0), and D(5, 3) 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. -parallel to $x = - 7$ , through $( 2,5 )$

Write an equation for the line described. Write the equation in the form specified. -perpendicular to x = 6, through (3, 5)

Graph the circle. - $x^{2}+(y-1)^{2}=4$ $Graph the circle. - x^{2}+(y-1)^{2}=4$

Match the description with the correct symbolic expression. -a linear equation whose graph has x-intercept -6 and y-intercept 6

Determine the intervals of the domain over which the function is continuous. -

Write an equation for the line described. Give your answer in slope-intercept form. -horizontal, through $( - 5 , - 3 )$

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - $f(x)=\frac{1}{4} x$ $Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - f(x)=\frac{1}{4} x$

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

Review of Basic Concepts

Filters

Exam 2: Graphs and Functions

Evaluate the function. -Find f(k)f ( k )f(k) when f(x)=3x2+4x+5f ( x ) = 3 x ^ { 2 } + 4 x + 5f(x)=3x2+4x+5

Graph the function. - f(x)={x2−9, if x<−10, if −1≤x≤1x2+9, if x>1f(x)=\left\{\begin{array}{ll}x^{2}-9, & \text { if } x<-1 \\0, & \text { if }-1 \leq x \leq 1 \\x^{2}+9, & \text { if } x>1\end{array}\right.f(x)=⎩⎨⎧​x2−9,0,x2+9,​ if x<−1 if −1≤x≤1 if x>1​

Find the specified domain. -Find the domain of (fg)(x)( f g ) ( x )(fg)(x) when f(x)=5x+4f ( x ) = \sqrt { 5 x + 4 }f(x)=5x+4​ and g(x)=5x−6g ( x ) = \sqrt { 5 x - 6 }g(x)=5x−6​

Evaluate the function. -Find g(a−1)g ( a - 1 )g(a−1) when g(x)=5x+2g ( x ) = 5 x + 2g(x)=5x+2

Use a graphing calculator to solve the linear equation. - (−8x−2)−7=−7(x+7)( - 8 x - 2 ) - 7 = - 7 ( x + 7 )(−8x−2)−7=−7(x+7)