Question 1

Evaluate the function.
-Find $g ( a - 1 )$ when $g ( x ) = \frac { 1 } { 2 } x + 3$

Accepted Answer

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

Question 2

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

Question 3

Determine whether the three points are collinear.
-(7, -3), (-3, 6), (1, 1)

Accepted Answer

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

Question 4

For the pair of functions, find the indicated sum, difference, product, or quotient.
-$$f ( x ) = 7 x - 5 , g ( x ) = 5 x - 8$$
Find $( f - g ) ( x )$.

Accepted Answer

A)  $12 x - 13$ 
B)  $2 x - 13$ 
C)  $- 2 x - 3$ 
D)  $2 x + 3$ 
A)  $12 x - 13$ 
B)  $2 x - 13$ 
C)  $- 2 x - 3$ 
D)  $2 x + 3$

Question 5

Find the slope and the y-intercept of the line.
-$$- 5 y = 4 x$$

Accepted Answer

A)  slope: $- \frac { 4 } { 5 } ; y$-intercept: $( 0,0 )$ 
B)  slope: $0 ; y$-intercept: $\left( 0 , - \frac { 4 } { 5 } \right)$ 
C)  slope: $- \frac { 5 } { 4 } ; y$-intercept: $( 0,0 )$ 
D)  slope: $0 ; y$-intercept: $\left( 0 , - \frac { 5 } { 4 } \right)$ 
A)  slope: $- \frac { 4 } { 5 } ; y$-intercept: $( 0,0 )$ 
B)  slope: $0 ; y$-intercept: $\left( 0 , - \frac { 4 } { 5 } \right)$ 
C)  slope: $- \frac { 5 } { 4 } ; y$-intercept: $( 0,0 )$ 
D)  slope: $0 ; y$-intercept: $\left( 0 , - \frac { 5 } { 4 } \right)$

Question 6

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

Accepted Answer

A)  $f ( x ) = \left\{ \begin{array} { l l } - 4 & \text { if } x \leq 1 \ - 3 & \text { if } x > 1 \end{array} \right.$; Domain: $( \infty , \infty )$, Range: $\{ - 4 , - 3 \}$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } - 4 & \text { if } x  1 \end{array} \right.$; Domain: $\{ - 4 , - 3 \}$, Range: $( \infty , \infty )$ 
A)  $f ( x ) = \left\{ \begin{array} { l l } - 4 & \text { if } x \leq 1 \ - 3 & \text { if } x > 1 \end{array} \right.$; Domain: $( \infty , \infty )$, Range: $\{ - 4 , - 3 \}$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } - 4 & \text { if } x  1 \end{array} \right.$; Domain: $\{ - 4 , - 3 \}$, Range: $( \infty , \infty )$

Question 7

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

Accepted Answer

A)  15 
B)  None of these 
C)  4 
D)  -1 
A)  15 
B)  None of these 
C)  4 
D)  -1

Question 8

Graph the function.
-$$f ( x ) = \left\{ \begin{array} { l l } 
- 3 , & \text { if } x \geq 1 \
- 5 - x , & \text { if } x < 1
\end{array} \right.$$

Accepted Answer

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

Question 9

The graph of $\mathrm { y } _ { 1 }$ is shown in the standard viewing window. Which is the only choice that could possibly be the solution of the equation $\mathrm { y } _ { 1 } = 0$ ?

- 
$$- 12 , - \frac { 13 } { 4 } , 3,12$$

Accepted Answer

A)  3 
B)  12 
C)  $- \frac { 13 } { 4 }$ 
D)  $- 12$ 
A)  3 
B)  12 
C)  $- \frac { 13 } { 4 }$ 
D)  $- 12$

Question 10

Find the slope of the line satisfying the given conditions.
-horizontal, through (9, 5)

Accepted Answer

A)  -1 
B)  0 
C)  undefined 
D)  1 
A)  -1 
B)  0 
C)  undefined 
D)  1

Question 11

The graph of $\mathrm { y } _ { 1 }$ is shown in the standard viewing window. Which is the only choice that could possibly be the solution of the equation $\mathrm { y } _ { 1 } = 0$ ?

-

$$- 12 , - 7 , - \frac { 13 } { 4 } , 12$$

Accepted Answer

A)  $- 7$ 
B)  12 
C)  $- 12$ 
D)  $- \frac { 13 } { 4 }$ 
A)  $- 7$ 
B)  12 
C)  $- 12$ 
D)  $- \frac { 13 } { 4 }$

Question 12

Write all linear equations in slope-intercept form.
-By reading a graph on defense spending in the country of Warpeas, you discover that in year 0 the country spent $42 million on defense and in year 8 spent $378 million. Write a linear function that
Relates y (in millions of dollars) to x.

Accepted Answer

A)  $y = \frac { 105 } { 2 } x + 42$ 
B)  $y = \frac { 1 } { 1 } x + 42$ 
C)  $y = 42 x + 42$ 
D)  $y = - 42 x - 42$ 
A)  $y = \frac { 105 } { 2 } x + 42$ 
B)  $y = \frac { 1 } { 1 } x + 42$ 
C)  $y = 42 x + 42$ 
D)  $y = - 42 x - 42$

Question 13

Find the center-radius form of the circle described or graphed.
-

Accepted Answer

A)  $( x + 5 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 9$ 
B)  $( x - 5 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 3$ 
C)  $( x + 5 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 3$ 
D)  $( x - 5 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 9$ 
A)  $( x + 5 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 9$ 
B)  $( x - 5 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 3$ 
C)  $( x + 5 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 3$ 
D)  $( x - 5 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 9$

Question 14

Graph the function.
-The charges for renting a moving van are $\$ 50$ for the first 50 miles and $\$ 5$ for each additional mile. Assume that a fraction of a mile is rounded up. (i) Determine the cost of driving the van 96 miles.
(ii) Find a symbolic representation for a function $\mathrm { f }$ that computes the cost of driving the van $\mathrm { x }$ miles, where $0 < x \leq 100$. (Hint: express $f$ as a piecewise-constant function.)

Accepted Answer

A)  $\$ 5030 ; f ( x ) = \left\{ \begin{array} { l l } 50 x & \text { if } 0 < x \leq 50 \ 50 + 5 ( x - 50 ) & \text { if } 50 < x \leq 100 \end{array} \right.$ 
B)  $\$ 780 ; f ( x ) = \left\{ \begin{array} { l l } 50 & \text { if } 0 < x \leq 50 \ 50 + 5 ( x + 50 ) & \text { if } 50 < x \leq 100 \end{array} \right.$ 
C)  $\$ 780 ; f ( x ) = \left\{ \begin{array} { l l } 50 & \text { if } 0 < x \leq 50 \ 50 + 5 ( x - 50 ) & \text { if } 50 < x \leq 100 \end{array} \right.$ 
D)  $\$ 280 ; f ( x ) = \left\{ \begin{array} { l l } 50 & \text { if } 0 < x \leq 50 \ 50 + 5 ( x - 50 ) & \text { if } 50 < x \leq 100 \end{array} \right.$ 
A)  $\$ 5030 ; f ( x ) = \left\{ \begin{array} { l l } 50 x & \text { if } 0 < x \leq 50 \ 50 + 5 ( x - 50 ) & \text { if } 50 < x \leq 100 \end{array} \right.$ 
B)  $\$ 780 ; f ( x ) = \left\{ \begin{array} { l l } 50 & \text { if } 0 < x \leq 50 \ 50 + 5 ( x + 50 ) & \text { if } 50 < x \leq 100 \end{array} \right.$ 
C)  $\$ 780 ; f ( x ) = \left\{ \begin{array} { l l } 50 & \text { if } 0 < x \leq 50 \ 50 + 5 ( x - 50 ) & \text { if } 50 < x \leq 100 \end{array} \right.$ 
D)  $\$ 280 ; f ( x ) = \left\{ \begin{array} { l l } 50 & \text { if } 0 < x \leq 50 \ 50 + 5 ( x - 50 ) & \text { if } 50 < x \leq 100 \end{array} \right.$

Question 15

Graph the circle.
-$$( x - 4 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 16$$

Accepted Answer

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

Question 16

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph.
-$$x ^ { 2 } + y ^ { 2 } - 2 x + 6 y - 15 = 0$$

Accepted Answer

A)  no; the graph is the point $( 1 , - 3 )$ 
B)  no; the graph is nonexistent 
C)  no; the graph is the point $( - 1,3 )$ 
D)  yes 
A)  no; the graph is the point $( 1 , - 3 )$ 
B)  no; the graph is nonexistent 
C)  no; the graph is the point $( - 1,3 )$ 
D)  yes

Question 17

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

Accepted Answer

A)  It is the graph of $f ( x ) = | x |$ translated 6 units to the left, stretched vertically by a factor of 2 and translated 8 units down. The equation is $y = 2 | x - 6 | + 8$ 
B)  It is the graph of $f ( x ) = | x |$ translated 6 units to the left, stretched vertically by a factor of 2 and translated 8 units down. The equation is $y = 2 | x + 6 | - 8$ 
C)  It is the graph of $f ( x ) = | x |$ translated 6 units to the left, shrunken vertically by a factor of $\frac { 1 } { 2 }$ and translated 8 units down. The equation is $y = \frac { 1 } { 2 } | x - 6 | - 8$ 
D)  It is the graph of $f ( x ) = | x |$ translated 6 units to the left, shrunken vertically by a factor of $\frac { 1 } { 2 }$ and translated 8 units down. The equation is $y = \frac { 1 } { 2 } | x + 6 | - 8$ 
A)  It is the graph of $f ( x ) = | x |$ translated 6 units to the left, stretched vertically by a factor of 2 and translated 8 units down. The equation is $y = 2 | x - 6 | + 8$ 
B)  It is the graph of $f ( x ) = | x |$ translated 6 units to the left, stretched vertically by a factor of 2 and translated 8 units down. The equation is $y = 2 | x + 6 | - 8$ 
C)  It is the graph of $f ( x ) = | x |$ translated 6 units to the left, shrunken vertically by a factor of $\frac { 1 } { 2 }$ and translated 8 units down. The equation is $y = \frac { 1 } { 2 } | x - 6 | - 8$ 
D)  It is the graph of $f ( x ) = | x |$ translated 6 units to the left, shrunken vertically by a factor of $\frac { 1 } { 2 }$ and translated 8 units down. The equation is $y = \frac { 1 } { 2 } | x + 6 | - 8$

Question 18

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

Accepted Answer

A)  $- 3 x ^ { 2 } + 2 x + 5$ 
B)  $- 3 x ^ { 2 } + 2 x - 5$ 
C)  $3 x ^ { 2 } + 2 x - 5$ 
D)  $3 x ^ { 2 } + 2 x + 5$ 
A)  $- 3 x ^ { 2 } + 2 x + 5$ 
B)  $- 3 x ^ { 2 } + 2 x - 5$ 
C)  $3 x ^ { 2 } + 2 x - 5$ 
D)  $3 x ^ { 2 } + 2 x + 5$

Question 19

Graph the line and give the domain and the range.
-$$x = 5$$

Accepted Answer

A)  $D = ( - \infty , \infty ) , R = \{ 5 \}$
  
B)  $D = ( - \infty , \infty ) , R = \{ 5 \}$
  
C)  $D = \{ 5 \} , R = ( - \infty , \infty )$
  
D)  $D = \{ 5 \} , R = ( - \infty , \infty )$
  
A)  $D = ( - \infty , \infty ) , R = \{ 5 \}$
  
B)  $D = ( - \infty , \infty ) , R = \{ 5 \}$
  
C)  $D = \{ 5 \} , R = ( - \infty , \infty )$
  
D)  $D = \{ 5 \} , R = ( - \infty , \infty )$

Question 20

Find the specified domain.
-Find the domain of $( f + g ) ( x )$ when $f ( x ) = \sqrt { 3 x - 9 }$ and $g ( x ) = \frac { 1 } { x }$

Accepted Answer

A)  $[ 3 , \infty )$ 
B)  $[ - 3 , \infty )$ 
C)  $[ - 3,0 ) \cup ( 0 , \infty )$ 
D)  $( \infty , 0 ) \cup ( 0 , \infty )$ 
A)  $[ 3 , \infty )$ 
B)  $[ - 3 , \infty )$ 
C)  $[ - 3,0 ) \cup ( 0 , \infty )$ 
D)  $( \infty , 0 ) \cup ( 0 , \infty )$

Evaluate the function. -Find $g ( a - 1 )$ when $g ( x ) = \frac { 1 } { 2 } x + 3$

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

Determine whether the three points are collinear. -(7, -3), (-3, 6), (1, 1)

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = 7 x - 5 , g ( x ) = 5 x - 8$ Find $( f - g ) ( x )$ .

Find the slope and the y-intercept of the line. - $- 5 y = 4 x$

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

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

Graph the function. - $f ( x ) = \left\{ \begin{array} { l l } - 3 , & \text { if } x \geq 1 \\- 5 - x , & \text { if } x < 1\end{array} \right.$ $Graph the function. - f ( x ) = \left\{ \begin{array} { l l } - 3 , & \text { if } x \geq 1 \\ - 5 - x , & \text { if } x < 1 \end{array} \right.$

Find the slope of the line satisfying the given conditions. -horizontal, through (9, 5)

Write all linear equations in slope-intercept form. -By reading a graph on defense spending in the country of Warpeas, you discover that in year 0 the country spent $42 million on defense and in year 8 spent $378 million. Write a linear function that Relates y (in millions of dollars) to x.

Find the center-radius form of the circle described or graphed. -

Graph the circle. - $( x - 4 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 16$ $Graph the circle. - ( x - 4 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 16$

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - $x ^ { 2 } + y ^ { 2 } - 2 x + 6 y - 15 = 0$

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

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

Graph the line and give the domain and the range. - $x = 5$

Find the specified domain. -Find the domain of $( f + g ) ( x )$ when $f ( x ) = \sqrt { 3 x - 9 }$ and $g ( x ) = \frac { 1 } { x }$

Review of Basic Concepts

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

Filters

Exam 3: Graphs and Functions

Evaluate the function. -Find g(a−1)g ( a - 1 )g(a−1) when g(x)=12x+3g ( x ) = \frac { 1 } { 2 } x + 3g(x)=21​x+3