Question 1

Graph the function.
-$$g ( x ) = - \sqrt { x + 2 } - 1$$

Accepted Answer

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

Question 2

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

Accepted Answer

A)  $( 4 , \infty )$ 
B)  $( - \infty , 4 ]$ 
C)  $[ 0 , \infty )$ 
D)  $( - \infty , \infty )$ 
A)  $( 4 , \infty )$ 
B)  $( - \infty , 4 ]$ 
C)  $[ 0 , \infty )$ 
D)  $( - \infty , \infty )$

Question 3

shown in the graph below. How high will the projectile be after 0.9 s?

Accepted Answer

A)  600 ft 
B)  550 ft 
C)  500 ft 
D)  450 ft
Answer: B
-The graph shows the relationship between current $\mathrm { I }$ and resistance $\mathrm { R }$ if the voltage is fixed. Find the current if the resistance is $2.5 \Omega$.
  
A)  1.0 A 
B)  0.6 A 
C)  0.8 A 
D)  1.2 A 
A)  600 ft 
B)  550 ft 
C)  500 ft 
D)  450 ft
Answer: B
-The graph shows the relationship between current $\mathrm { I }$ and resistance $\mathrm { R }$ if the voltage is fixed. Find the current if the resistance is $2.5 \Omega$.
  
A)  1.0 A 
B)  0.6 A 
C)  0.8 A 
D)  1.2 A

Question 4

Decide whether the relation defines a function.
-

Accepted Answer

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

Question 5

An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x).
-$$y - 3 x ^ { 2 } = 8 - x$$

Accepted Answer

A)  $f ( x ) = 3 x ^ { 2 } + x + 8$ 
B)  $f ( x ) = - 3 x ^ { 2 } + x - 8$ 
C)  $f ( x ) = 3 x ^ { 2 } - x + 8$ 
D)  $f ( x ) = - 3 x ^ { 2 } - x + 8$ 
A)  $f ( x ) = 3 x ^ { 2 } + x + 8$ 
B)  $f ( x ) = - 3 x ^ { 2 } + x - 8$ 
C)  $f ( x ) = 3 x ^ { 2 } - x + 8$ 
D)  $f ( x ) = - 3 x ^ { 2 } - x + 8$

Question 6

Write an equation for the line described. Write the equation in the form specified.
-parallel to $4 x + 7 y = - 17$; through $( 8 , - 13 )$; standard form

Accepted Answer

A)  $7 x + 4 y = - 13$ 
B)  $4 x - 7 y = - 59$ 
C)  $4 x + 7 y = - 59$ 
D)  $8 x + 7 y = - 17$ 
A)  $7 x + 4 y = - 13$ 
B)  $4 x - 7 y = - 59$ 
C)  $4 x + 7 y = - 59$ 
D)  $8 x + 7 y = - 17$

Question 7

Find the center-radius form of the circle described or graphed.
-The locations of three receiving stations and the distances to the epicenter of an earthquake are contained in the following three equations: $( x + 2 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 16 , ( x + 7 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 25$ $( x - 4 ) ^ { 2 } + ( y + 11 ) ^ { 2 } = 100$. Determine the location of the epicenter.

Accepted Answer

A)  at $( - 1 , - 4 )$ 
B)  at $( - 3 , - 1 )$ 
C)  at $( - 2 , - 3 )$ 
D)  at $( - 1 , - 3 )$ 
A)  at $( - 1 , - 4 )$ 
B)  at $( - 3 , - 1 )$ 
C)  at $( - 2 , - 3 )$ 
D)  at $( - 1 , - 3 )$

Question 8

Graph the function.
-$f(x)=-2|x|$

Accepted Answer

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

Question 9

Graph the function.
-$y=|x+5|+3$

Accepted Answer

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

Question 10

Graph the line described.
-$$\text { through } ( 10,0 ) ; m = - \frac { 1 } { 2 }$$

Accepted Answer

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

Question 11

Evaluate the function.
-Find $f ( 0 )$ when $f ( x ) = x ^ { 2 } - 2 x - 3$

Accepted Answer

A)  9 
B)  3 
C)  0 
D)  $- 3$ 
A)  9 
B)  3 
C)  0 
D)  $- 3$

Question 12

Compute and simplify the difference quotient $$\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$$
-$$f ( x ) = 6 x ^ { 2 } + 5 x$$

Accepted Answer

A)  $18 x - 8 h + 10$ 
B)  $12 x + 5$ 
C)  $12 x ^ { 2 } + 6 h + 5 x$ 
D)  $12 x + 6 h + 5$ 
A)  $18 x - 8 h + 10$ 
B)  $12 x + 5$ 
C)  $12 x ^ { 2 } + 6 h + 5 x$ 
D)  $12 x + 6 h + 5$

Question 13

Graph the point symmetric to the given point.
-$$\text { Plot the point } ( 1,2 ) \text {, then plot the point that is symmetric to } ( 1,2 ) \text { with respect to the } y \text {-axis. }$$

Accepted Answer

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

Question 14

Determine if the function is even, odd, or neither.
-$f ( x ) = - 8 x ^ { 4 } + 6 x + 3$

Accepted Answer

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

Question 15

Determine if the function is even, odd, or neither.
-$$f ( x ) = 3 x ^ { 2 } + 1$$

Accepted Answer

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

Question 16

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)  $y = \frac { x } { - 6 }$ 
B)  $y = - 6 x$ 
C)  $y = 6 x$ 
D)  $y = \frac { x } { 6 }$ 
A)  $y = \frac { x } { - 6 }$ 
B)  $y = - 6 x$ 
C)  $y = 6 x$ 
D)  $y = \frac { x } { 6 }$

Question 17

Find the specified domain.
-Use the tables to find (fg)(1).
$\begin{array}{l}
\begin{array}{r|c|c|c}
x & 1 & 2 & 5 \
\hline f(x) & -6 & 5 & -9
\end{array}\
\begin{array}{r|c|c|c}
\mathrm{x} & 1 & 4 & 5 \
\hline \mathrm{g}(\mathrm{x}) & 9 & -4 & -8
\end{array}
\end{array}$

Accepted Answer

A)  72 
B)  1 
C)  $- 20$ 
D)  $- 54$ 
A)  72 
B)  1 
C)  $- 20$ 
D)  $- 54$

Question 18

Write an equation for the line described. Write the equation in the form specified.
-parallel to x = 3, through (9, 5)

Accepted Answer

A)  y = 3 
B)  x = 9 
C)  y = 5 
D)  x = 5 
A)  y = 3 
B)  x = 9 
C)  y = 5 
D)  x = 5

Question 19

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

Accepted Answer

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

Question 20

For the points P and Q, find the coordinates of the midpoint of the segment PQ.
-$$P ( - 5 , - 7 ) , Q ( 1,8 )$$

Accepted Answer

A)  $\left( - 2 , \frac { 1 } { 2 } \right)$ 
B)  $\left( - 3 , - \frac { 15 } { 2 } \right)$ 
C)  $( - 4,1 )$ 
D)  $( - 6 , - 15 )$ 
A)  $\left( - 2 , \frac { 1 } { 2 } \right)$ 
B)  $\left( - 3 , - \frac { 15 } { 2 } \right)$ 
C)  $( - 4,1 )$ 
D)  $( - 6 , - 15 )$

Graph the function. - $g ( x ) = - \sqrt { x + 2 } - 1$ $Graph the function. - g ( x ) = - \sqrt { x + 2 } - 1$

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

Decide whether the relation defines a function. -

An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x). - $y - 3 x ^ { 2 } = 8 - x$

Write an equation for the line described. Write the equation in the form specified. -parallel to $4 x + 7 y = - 17$ ; through $( 8 , - 13 )$ ; standard form

Graph the function. - $f(x)=-2|x|$

Graph the function. - $y=|x+5|+3$

Graph the line described. - $\text { through } ( 10,0 ) ; m = - \frac { 1 } { 2 }$ $Graph the line described. - \text { through } ( 10,0 ) ; m = - \frac { 1 } { 2 }$

Evaluate the function. -Find $f ( 0 )$ when $f ( x ) = x ^ { 2 } - 2 x - 3$

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$ - $f ( x ) = 6 x ^ { 2 } + 5 x$

Determine if the function is even, odd, or neither. - $f ( x ) = - 8 x ^ { 4 } + 6 x + 3$

Determine if the function is even, odd, or neither. - $f ( x ) = 3 x ^ { 2 } + 1$

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

Find the specified domain. -Use the tables to find (fg)(1). x 1 2 5 f(x) -6 5 -9 1 4 5 () 9 -4 -8

Write an equation for the line described. Write the equation in the form specified. -parallel to x = 3, through (9, 5)

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

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $P ( - 5 , - 7 ) , Q ( 1,8 )$

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

Graph the function. - g(x)=−x+2−1g ( x ) = - \sqrt { x + 2 } - 1g(x)=−x+2​−1

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

Decide whether the relation defines a function. -

An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x). - y−3x2=8−xy - 3 x ^ { 2 } = 8 - xy−3x2=8−x

Write an equation for the line described. Write the equation in the form specified. -parallel to 4x+7y=−174 x + 7 y = - 174x+7y=−17 ; through (8,−13)( 8 , - 13 )(8,−13) ; standard form

Graph the function. - f(x)=−2∣x∣f(x)=-2|x|f(x)=−2∣x∣

Graph the function. - y=∣x+5∣+3y=|x+5|+3y=∣x+5∣+3

Graph the line described. - through (10,0);m=−12\text { through } ( 10,0 ) ; m = - \frac { 1 } { 2 } through (10,0);m=−21​

Evaluate the function. -Find f(0)f ( 0 )f(0) when f(x)=x2−2x−3f ( x ) = x ^ { 2 } - 2 x - 3f(x)=x2−2x−3

Compute and simplify the difference quotient f(x+h)−f(x)h,h≠0\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0hf(x+h)−f(x)​,h=0 - f(x)=6x2+5xf ( x ) = 6 x ^ { 2 } + 5 xf(x)=6x2+5x

Determine if the function is even, odd, or neither. - f(x)=−8x4+6x+3f ( x ) = - 8 x ^ { 4 } + 6 x + 3f(x)=−8x4+6x+3

Determine if the function is even, odd, or neither. - f(x)=3x2+1f ( x ) = 3 x ^ { 2 } + 1f(x)=3x2+1

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

Find the specified domain. -Use the tables to find (fg)(1). x 1 2 5 f(x) -6 5 -9 1 4 5 () 9 -4 -8

Write an equation for the line described. Write the equation in the form specified. -parallel to x = 3, through (9, 5)

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - P(−5,−7),Q(1,8)P ( - 5 , - 7 ) , Q ( 1,8 )P(−5,−7),Q(1,8)

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

Graph the function. - $g ( x ) = - \sqrt { x + 2 } - 1$ $Graph the function. - g ( x ) = - \sqrt { x + 2 } - 1$

An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x). - $y - 3 x ^ { 2 } = 8 - x$

Write an equation for the line described. Write the equation in the form specified. -parallel to $4 x + 7 y = - 17$ ; through $( 8 , - 13 )$ ; standard form

Graph the function. - $f(x)=-2|x|$

Graph the function. - $y=|x+5|+3$

Graph the line described. - $\text { through } ( 10,0 ) ; m = - \frac { 1 } { 2 }$ $Graph the line described. - \text { through } ( 10,0 ) ; m = - \frac { 1 } { 2 }$

Evaluate the function. -Find $f ( 0 )$ when $f ( x ) = x ^ { 2 } - 2 x - 3$

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$ - $f ( x ) = 6 x ^ { 2 } + 5 x$

Determine if the function is even, odd, or neither. - $f ( x ) = - 8 x ^ { 4 } + 6 x + 3$

Determine if the function is even, odd, or neither. - $f ( x ) = 3 x ^ { 2 } + 1$

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $P ( - 5 , - 7 ) , Q ( 1,8 )$