Question 1

Describe the transformations and give the equation for the graph.
-Find $\left( \frac { f } { g } \right) ( - 4 )$ when $f ( x ) = 4 x - 3$ and $g ( x ) = 2 x ^ { 2 } + 14 x + 4$

Accepted Answer

A)  $\frac { 19 } { 20 }$ 
B)  $- \frac { 1 } { 10 }$ 
C)  $- \frac { 1 } { 5 }$ 
D)  $\frac { 2 } { 13 }$ 
A)  $\frac { 19 } { 20 }$ 
B)  $- \frac { 1 } { 10 }$ 
C)  $- \frac { 1 } { 5 }$ 
D)  $\frac { 2 } { 13 }$

Question 2

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)  $y = - 1$ 
B)  $x = - 1$ 
C)  $x = 1$ 
D)  $y = 1$ 
A)  $y = - 1$ 
B)  $x = - 1$ 
C)  $x = 1$ 
D)  $y = 1$

Question 3

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$
-$$\text { Select the equation that describes the graph shown. }$$
 
 An

Accepted Answer

A)  $y = x ^ { 2 } - 2$ 
B)  $y = ( x + 2 ) ^ { 2 }$ 
C)  $y = ( x - 2 ) ^ { 2 }$ 
D)  $y = ( x - 2 ) ^ { 2 } + 2$ swer: A 
A)  $y = x ^ { 2 } - 2$ 
B)  $y = ( x + 2 ) ^ { 2 }$ 
C)  $y = ( x - 2 ) ^ { 2 }$ 
D)  $y = ( x - 2 ) ^ { 2 } + 2$ swer: A

Question 4

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)  $y = - \frac { 1 } { 5 } x$ 
B)  $y = 5 x$ 
C)  $y = \frac { 1 } { 5 } x$ 
D)  $y = - 5 x$ 
A)  $y = - \frac { 1 } { 5 } x$ 
B)  $y = 5 x$ 
C)  $y = \frac { 1 } { 5 } x$ 
D)  $y = - 5 x$

Question 5

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

Accepted Answer

A) $f ( x ) = \left\{ \begin{array} { l l } 4 & \text { if } x \leq 0 \ - x & \text { if } x > 0 \end{array} \right.$; Domain: $( \infty , \infty )$, Range: $( \infty , 0 ) \cup \{ 4 \}$ B) $f ( x ) = \left\{ \begin{array} { l l } 4 & \text { if } x < 0 \ - 4 x & \text { if } x \geq 0 \end{array} \right.$; Domain: $( \infty , 0 ) \cup \{ 4 \}$, Range: $( \infty , \infty )$ C) $f ( x ) = \left\{ \begin{array} { l l } 4 & \text { if } x < 0 \ x & \text { if } x \geq 0 \end{array} \right.$; Domain: $( \infty , 0 ] \cup ( 4 )$, Range: $( \infty , \infty )$ D) $f ( x ) = \left\{ \begin{array} { l l } 4 & \text { if } x < 0 \ - x & \text { if } x \geq 0 \end{array} \right.$; Domain: $( \infty , \infty )$, Range: $( \infty , 0 ] \cup \{ 4 \}$ A) $f ( x ) = \left\{ \begin{array} { l l } 4 & \text { if } x \leq 0 \ - x & \text { if } x > 0 \end{array} \right.$; Domain: $( \infty , \infty )$, Range: $( \infty , 0 ) \cup \{ 4 \}$ B) $f ( x ) = \left\{ \begin{array} { l l } 4 & \text { if } x < 0 \ - 4 x & \text { if } x \geq 0 \end{array} \right.$; Domain: $( \infty , 0 ) \cup \{ 4 \}$, Range: $( \infty , \infty )$ C) $f ( x ) = \left\{ \begin{array} { l l } 4 & \text { if } x < 0 \ x & \text { if } x \geq 0 \end{array} \right.$; Domain: $( \infty , 0 ] \cup ( 4 )$, Range: $( \infty , \infty )$ D) $f ( x ) = \left\{ \begin{array} { l l } 4 & \text { if } x < 0 \ - x & \text { if } x \geq 0 \end{array} \right.$; Domain: $( \infty , \infty )$, Range: $( \infty , 0 ] \cup \{ 4 \}$

Question 6

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-midpoint (b, x), endpoint (m, q)

Accepted Answer

A)  $( 2 b - m , 2 x - q )$ 
B)  $\left( \frac { b + m } { 2 } , \frac { x + q } { 2 } \right)$ 
C)  $( b - m , x - q )$ 
D)  $( 2 m - b , 2 q - x )$ 
A)  $( 2 b - m , 2 x - q )$ 
B)  $\left( \frac { b + m } { 2 } , \frac { x + q } { 2 } \right)$ 
C)  $( b - m , x - q )$ 
D)  $( 2 m - b , 2 q - x )$

Question 7

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.  
-At what time was the temperature 79°?

Accepted Answer

A)  12 p.m. 
B)  4 p.m. 
C)  3 p.m. 
D)  1 p.m. 
A)  12 p.m. 
B)  4 p.m. 
C)  3 p.m. 
D)  1 p.m.

Question 8

Determine if the function is even, odd, or neither.
-$f ( x ) = 0.5 x ^ { 2 } + | x | + 3$

Accepted Answer

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

Question 9

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph.
-$$x ^ { 2 } + y ^ { 2 } + 18 x + 14 y + 211 = 0$$

Accepted Answer

A)  yes 
B)  no; the graph is nonexistent 
C)  no; the graph is the point $( 9,7 )$ 
D)  no; the graph is the point $( - 9 , - 7 )$ 
A)  yes 
B)  no; the graph is nonexistent 
C)  no; the graph is the point $( 9,7 )$ 
D)  no; the graph is the point $( - 9 , - 7 )$

Question 10

Graph the function.
-$$f ( x ) = 3 ( x + 1 ) ^ { 2 } - 3$$

Accepted Answer

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

Question 11

Refer to the following graphs to determine an appropriate response.  
-Which is not the graph of a function? What is its equation?

Accepted Answer

A)  graph B; $x = y ^ { 2 }$ 
B)  graph $C ; y = \sqrt { x }$ 
C)  graph A; $y = x$ 
D)  graph D; $y = [ [ x ] ]$ 
A)  graph B; $x = y ^ { 2 }$ 
B)  graph $C ; y = \sqrt { x }$ 
C)  graph A; $y = x$ 
D)  graph D; $y = [ [ x ] ]$

Question 12

Find the center-radius form of the equation of the circle.
-center $( 7,0 )$, radius $\sqrt { 15 }$

Accepted Answer

A)  $( x + 7 ) ^ { 2 } + y ^ { 2 } = 15$ 
B)  $( x - 7 ) ^ { 2 } + y ^ { 2 } = \sqrt { 15 }$ 
C)  $( x - 7 ) ^ { 2 } + y ^ { 2 } = 15$ 
D)  $x ^ { 2 } + ( y - 7 ) ^ { 2 } = 225$ 
A)  $( x + 7 ) ^ { 2 } + y ^ { 2 } = 15$ 
B)  $( x - 7 ) ^ { 2 } + y ^ { 2 } = \sqrt { 15 }$ 
C)  $( x - 7 ) ^ { 2 } + y ^ { 2 } = 15$ 
D)  $x ^ { 2 } + ( y - 7 ) ^ { 2 } = 225$

Question 13

Find the center-radius form of the equation of the circle.
-center $( 0,0 )$, radius 3

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } = 9$ 
B)  $x ^ { 2 } + y ^ { 2 } = 3$ 
C)  $x ^ { 2 } + y ^ { 2 } = \sqrt { 3 }$ 
D)  $x ^ { 2 } + y ^ { 2 } = 6$ 
A)  $x ^ { 2 } + y ^ { 2 } = 9$ 
B)  $x ^ { 2 } + y ^ { 2 } = 3$ 
C)  $x ^ { 2 } + y ^ { 2 } = \sqrt { 3 }$ 
D)  $x ^ { 2 } + y ^ { 2 } = 6$

Question 14

Graph the function.
-$f(x)=4 \sqrt{x}$

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

Graph the line and give the domain and the range.
-$$4 x - 12 y = 24$$

Accepted Answer

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

Question 17

Graph the function.
-$f(x)=\frac{1}{6}|-x|$

Accepted Answer

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

Question 18

Determine whether the three points are collinear.
-(-5, -11), (4, 7), (5, 9)

Accepted Answer

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

Question 19

Graph the circle.
-$$x ^ { 2 } + y ^ { 2 } = 36$$

Accepted Answer

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

Question 20

Graph the equation by plotting points.
-$y=\sqrt{x+1}$

Accepted Answer

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

Describe the transformations and give the equation for the graph. -Find $\left( \frac { f } { g } \right) ( - 4 )$ when $f ( x ) = 4 x - 3$ and $g ( x ) = 2 x ^ { 2 } + 14 x + 4$

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

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

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

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint (b, x), endpoint (m, q)

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport. -At what time was the temperature 79°?

Determine if the function is even, odd, or neither. - $f ( x ) = 0.5 x ^ { 2 } + | x | + 3$

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - $x ^ { 2 } + y ^ { 2 } + 18 x + 14 y + 211 = 0$

Graph the function. - $f ( x ) = 3 ( x + 1 ) ^ { 2 } - 3$ $Graph the function. - f ( x ) = 3 ( x + 1 ) ^ { 2 } - 3$

Refer to the following graphs to determine an appropriate response. -Which is not the graph of a function? What is its equation?

Find the center-radius form of the equation of the circle. -center $( 7,0 )$ , radius $\sqrt { 15 }$

Find the center-radius form of the equation of the circle. -center $( 0,0 )$ , radius 3

Graph the function. - $f(x)=4 \sqrt{x}$ $Graph the function. - f(x)=4 \sqrt{x}$

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

Graph the line and give the domain and the range. - $4 x - 12 y = 24$

Graph the function. - $f(x)=\frac{1}{6}|-x|$ $Graph the function. - f(x)=\frac{1}{6}|-x|$

Determine whether the three points are collinear. -(-5, -11), (4, 7), (5, 9)

Graph the circle. - $x ^ { 2 } + y ^ { 2 } = 36$ $Graph the circle. - x ^ { 2 } + y ^ { 2 } = 36$

Graph the equation by plotting points. - $y=\sqrt{x+1}$ $Graph the equation by plotting points. - y=\sqrt{x+1}$

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

Describe the transformations and give the equation for the graph. -Find (fg)(−4)\left( \frac { f } { g } \right) ( - 4 )(gf​)(−4) when f(x)=4x−3f ( x ) = 4 x - 3f(x)=4x−3 and g(x)=2x2+14x+4g ( x ) = 2 x ^ { 2 } + 14 x + 4g(x)=2x2+14x+4

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

Describe how the graph of the equation relates to the graph of y y=x3y = \sqrt [ 3 ] { x }y=3x​ - Select the equation that describes the graph shown. \text { Select the equation that describes the graph shown. } Select the equation that describes the graph shown. An

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

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

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint (b, x), endpoint (m, q)

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport. -At what time was the temperature 79°?

Determine if the function is even, odd, or neither. - f(x)=0.5x2+∣x∣+3f ( x ) = 0.5 x ^ { 2 } + | x | + 3f(x)=0.5x2+∣x∣+3

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - x2+y2+18x+14y+211=0x ^ { 2 } + y ^ { 2 } + 18 x + 14 y + 211 = 0x2+y2+18x+14y+211=0

Graph the function. - f(x)=3(x+1)2−3f ( x ) = 3 ( x + 1 ) ^ { 2 } - 3f(x)=3(x+1)2−3

Refer to the following graphs to determine an appropriate response. -Which is not the graph of a function? What is its equation?

Find the center-radius form of the equation of the circle. -center (7,0)( 7,0 )(7,0) , radius 15\sqrt { 15 }15​

Find the center-radius form of the equation of the circle. -center (0,0)( 0,0 )(0,0) , radius 3

Graph the function. - f(x)=4xf(x)=4 \sqrt{x}f(x)=4x​

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 line and give the domain and the range. - 4x−12y=244 x - 12 y = 244x−12y=24

Graph the function. - f(x)=16∣−x∣f(x)=\frac{1}{6}|-x|f(x)=61​∣−x∣

Determine whether the three points are collinear. -(-5, -11), (4, 7), (5, 9)

Graph the circle. - x2+y2=36x ^ { 2 } + y ^ { 2 } = 36x2+y2=36

Graph the equation by plotting points. - y=x+1y=\sqrt{x+1}y=x+1​

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

Describe the transformations and give the equation for the graph. -Find $\left( \frac { f } { g } \right) ( - 4 )$ when $f ( x ) = 4 x - 3$ and $g ( x ) = 2 x ^ { 2 } + 14 x + 4$

Determine if the function is even, odd, or neither. - $f ( x ) = 0.5 x ^ { 2 } + | x | + 3$

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - $x ^ { 2 } + y ^ { 2 } + 18 x + 14 y + 211 = 0$

Graph the function. - $f ( x ) = 3 ( x + 1 ) ^ { 2 } - 3$ $Graph the function. - f ( x ) = 3 ( x + 1 ) ^ { 2 } - 3$

Find the center-radius form of the equation of the circle. -center $( 7,0 )$ , radius $\sqrt { 15 }$

Find the center-radius form of the equation of the circle. -center $( 0,0 )$ , radius 3

Graph the function. - $f(x)=4 \sqrt{x}$ $Graph the function. - f(x)=4 \sqrt{x}$

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

Graph the line and give the domain and the range. - $4 x - 12 y = 24$

Graph the function. - $f(x)=\frac{1}{6}|-x|$ $Graph the function. - f(x)=\frac{1}{6}|-x|$

Graph the circle. - $x ^ { 2 } + y ^ { 2 } = 36$ $Graph the circle. - x ^ { 2 } + y ^ { 2 } = 36$

Graph the equation by plotting points. - $y=\sqrt{x+1}$ $Graph the equation by plotting points. - y=\sqrt{x+1}$