Question 1

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.  
-During which hour did the temperature increase the most?

Accepted Answer

A)  1 p.m. to 2 p.m. 
B)  12 p.m. to 1 p.m. 
C)  10 a.m. to 11 a.m. 
D)  9 a.m. to 10 a.m. 
A)  1 p.m. to 2 p.m. 
B)  12 p.m. to 1 p.m. 
C)  10 a.m. to 11 a.m. 
D)  9 a.m. to 10 a.m.

Question 2

For the given functions f and g , find the indicated composition.
-$f(x)=4 x+15, \quad g(x)=4 x-1$
$(f \circ g)(x)$

Accepted Answer

A)  $16 x + 19$ 
B)  $16 x + 14$ 
C)  $16 x + 11$ 
D)  $16 x + 59$ 
A)  $16 x + 19$ 
B)  $16 x + 14$ 
C)  $16 x + 11$ 
D)  $16 x + 59$

Question 3

Describe how the graph of the equation relates to the graph of y $y = x ^ { 2 }$
-$$f ( x ) = ( x - 5 ) ^ { 2 } + 9$$

Accepted Answer

A)  a translation 5 units to the left and 9 units up 
B)  a translation 9 units to the right and 5 units up 
C)  a translation 5 units to the left and 9 units down 
D)  a translation 5 units to the right and 9 units up 
A)  a translation 5 units to the left and 9 units up 
B)  a translation 9 units to the right and 5 units up 
C)  a translation 5 units to the left and 9 units down 
D)  a translation 5 units to the right and 9 units up

Question 4

Find the average rate of change illustrated in the graph.
- 
Usage (in minutes)

Accepted Answer

A)  $\$ 0.50$ per minute 
B)  $\$ 0.25$ per minute 
C)  $\$ 4.00$ per minute 
D)  $\$ 2.00$ per minute 
A)  $\$ 0.50$ per minute 
B)  $\$ 0.25$ per minute 
C)  $\$ 4.00$ per minute 
D)  $\$ 2.00$ per minute

Question 5

Determine whether the three points are the vertices of a right triangle.
-(5, 6), (7, 10), (9, 9)

Accepted Answer

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

Question 6

For the given functions f and g , find the indicated composition.
-$$f ( x ) = 4 x ^ { 2 } + 5 x + 7 , \quad g ( x ) = 5 x - 6$$

Accepted Answer

A)  $20 x ^ { 2 } + 25 x + 29$ 
B)  $20 x ^ { 2 } + 25 x + 41$ 
C)  $4 x ^ { 2 } + 5 x + 1$ 
D)  $4 x ^ { 2 } + 25 x + 29$ 
A)  $20 x ^ { 2 } + 25 x + 29$ 
B)  $20 x ^ { 2 } + 25 x + 41$ 
C)  $4 x ^ { 2 } + 5 x + 1$ 
D)  $4 x ^ { 2 } + 25 x + 29$

Question 7

Find the average rate of change illustrated in the graph.
-The linear function $f ( x ) = 1.8 x + 22$ models the percentage of people, $f ( x )$, who graduated from college $x$ years after 1998. Find and interpret the slope.

Accepted Answer

A)  $\mathrm { m } = 1.8$; the percentage of people graduating from college has decreased at a rate of $1.8 \%$ per year since 1998 . 
B)  $\mathrm { m } = 22$; the percentage of people graduating from college has increased at a rate of $22 \%$ per year since 1998 . 
C)  $\mathrm { m } = 1.8$; the percentage of people graduating from college has increased at a rate of $1.8 \%$ per year since 1998 . 
D)  $m = - 1.8$; the percentage of people graduating from college has decreased at a rate of $1.8 \%$ per year since 1998 . 
A)  $\mathrm { m } = 1.8$; the percentage of people graduating from college has decreased at a rate of $1.8 \%$ per year since 1998 . 
B)  $\mathrm { m } = 22$; the percentage of people graduating from college has increased at a rate of $22 \%$ per year since 1998 . 
C)  $\mathrm { m } = 1.8$; the percentage of people graduating from college has increased at a rate of $1.8 \%$ per year since 1998 . 
D)  $m = - 1.8$; the percentage of people graduating from college has decreased at a rate of $1.8 \%$ per year since 1998 .

Question 8

Describe how the graph of the equation relates to the graph of y $y = x ^ { 2 }$
-$$f ( x ) = \frac { 1 } { 5 } x ^ { 2 } - 3$$

Accepted Answer

A)  vertical stretching by a factor of 5 and a translation 3 units to the right 
B)  vertical shrinking by a factor of $\frac { 1 } { 5 }$ and a translation 3 units to the left 
C)  vertical shrinking by a factor of $\frac { 1 } { 5 }$ and a translation 3 units down 
D)  vertical stretching by a factor of 5 and a translation 3 units down 
A)  vertical stretching by a factor of 5 and a translation 3 units to the right 
B)  vertical shrinking by a factor of $\frac { 1 } { 5 }$ and a translation 3 units to the left 
C)  vertical shrinking by a factor of $\frac { 1 } { 5 }$ and a translation 3 units down 
D)  vertical stretching by a factor of 5 and a translation 3 units down

Question 9

Graph the function.
-$f(x)=2 \llbracket x \rrbracket$

Accepted Answer

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

Question 10

Graph the function.
-$y=\sqrt{x-6}+7$

Accepted Answer

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

Question 11

Find the specified domain.
-The graphs of functions $f$ and $g$ are shown. Use these graphs to find $( f + g ) ( - 2 )$.

Accepted Answer

A)  4 
B)  $- 3$ 
C)  5 
D)  $\frac { 1 } { 4 }$ 
A)  4 
B)  $- 3$ 
C)  5 
D)  $\frac { 1 } { 4 }$

Question 12

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.
-$$y = 3 x ^ { 2 } + 4$$

Accepted Answer

A)  $x$-axis, $y$-axis, origin 
B)  $x$-axis only 
C)  $y$-axis only 
D)  origin only 
A)  $x$-axis, $y$-axis, origin 
B)  $x$-axis only 
C)  $y$-axis only 
D)  origin only

Question 13

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

Accepted Answer

A) $f ( x ) = \left\{ \begin{array} { l l } - 5 & \text { if } x \leq 0 \ 5 & \text { if } x > 0 \end{array} \right.$; Domain: $\{ - 5,5 \}$, Range: $( \infty , \infty )$ B) $f ( x ) = \left\{ \begin{array} { l l } 5 & \text { if } x \leq 0 \ - 5 & \text { if } x > 0 \end{array} \right.$; Domain: $( \infty , \infty )$, Range: $\{ - 5,5 \}$ C) $f ( x ) = \left\{ \begin{array} { l l } 5 x & \text { if } x \leq 0 \ - 5 x & \text { if } x > 0 \end{array} \right.$; Domain: $\{ - 5,5 \}$, Range: $( \infty , \infty )$ D) $f ( x ) = \left\{ \begin{array} { l l } 5 & \text { if } x < 0 \ - 5 & \text { if } x \geq 0 \end{array} \right.$; Domain: $( \infty , \infty )$, Range: $\{ - 5,5 \}$ A) $f ( x ) = \left\{ \begin{array} { l l } - 5 & \text { if } x \leq 0 \ 5 & \text { if } x > 0 \end{array} \right.$; Domain: $\{ - 5,5 \}$, Range: $( \infty , \infty )$ B) $f ( x ) = \left\{ \begin{array} { l l } 5 & \text { if } x \leq 0 \ - 5 & \text { if } x > 0 \end{array} \right.$; Domain: $( \infty , \infty )$, Range: $\{ - 5,5 \}$ C) $f ( x ) = \left\{ \begin{array} { l l } 5 x & \text { if } x \leq 0 \ - 5 x & \text { if } x > 0 \end{array} \right.$; Domain: $\{ - 5,5 \}$, Range: $( \infty , \infty )$ D) $f ( x ) = \left\{ \begin{array} { l l } 5 & \text { if } x < 0 \ - 5 & \text { if } x \geq 0 \end{array} \right.$; Domain: $( \infty , \infty )$, Range: $\{ - 5,5 \}$

Question 14

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

Accepted Answer

A)  $( x - 3 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 2$ 
B)  $( x + 3 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 4$ 
C)  $( x - 3 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 4$ 
D)  $( x + 3 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 2$ 
A)  $( x - 3 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 2$ 
B)  $( x + 3 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 4$ 
C)  $( x - 3 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 4$ 
D)  $( x + 3 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 2$

Question 15

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)  $y = 3 x + 5$ 
B)  $y = - 3 x + 5$ 
C)  $y = 3 x - 5$ 
D)  $y = - 3 x - 5$ 
A)  $y = 3 x + 5$ 
B)  $y = - 3 x + 5$ 
C)  $y = 3 x - 5$ 
D)  $y = - 3 x - 5$

Question 16

Determine if the function is even, odd, or neither.
-$f ( x ) = - 8 x ^ { 3 } + 5 x ^ { 2 } - 2$

Accepted Answer

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

Question 17

Find the center-radius form of the equation of the circle.
-center $( 0,2 )$, radius $\sqrt { 19 }$

Accepted Answer

A)  $( x + 2 ) ^ { 2 } + y ^ { 2 } = 361$ 
B)  $x ^ { 2 } + ( y + 2 ) ^ { 2 } = 19$ 
C)  $( x - 2 ) ^ { 2 } + y ^ { 2 } = 361$ 
D)  $x ^ { 2 } + ( y - 2 ) ^ { 2 } = 19$ 
A)  $( x + 2 ) ^ { 2 } + y ^ { 2 } = 361$ 
B)  $x ^ { 2 } + ( y + 2 ) ^ { 2 } = 19$ 
C)  $( x - 2 ) ^ { 2 } + y ^ { 2 } = 361$ 
D)  $x ^ { 2 } + ( y - 2 ) ^ { 2 } = 19$

Question 18

Graph the function.
-$$f ( x ) = \frac { 1 } { 5 } \sqrt { - x }$$

Accepted Answer

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

Question 19

Find the center-radius form of the circle described or graphed.
-a circle having a diameter with endpoints $( - 2,8 )$ and $( 8,2 )$

Accepted Answer

A)  $( x - 3 ) ^ { 2 } + y ^ { 2 } = 9$ 
B)  $( x - 3 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 34$ 
C)  $x ^ { 2 } + ( y - 5 ) ^ { 2 } = 25$ 
D)  $( x - 5 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 34$ 
A)  $( x - 3 ) ^ { 2 } + y ^ { 2 } = 9$ 
B)  $( x - 3 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 34$ 
C)  $x ^ { 2 } + ( y - 5 ) ^ { 2 } = 25$ 
D)  $( x - 5 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 34$

Question 20

Find the slope of the line satisfying the given conditions.
-through $( - 6 , - 7 )$ and $( 5,1 )$

Accepted Answer

A)  $\frac { 11 } { 8 }$ 
B)  $- \frac { 11 } { 8 }$ 
C)  $- \frac { 8 } { 11 }$ 
D)  $\frac { 8 } { 11 }$ 
A)  $\frac { 11 } { 8 }$ 
B)  $- \frac { 11 } { 8 }$ 
C)  $- \frac { 8 } { 11 }$ 
D)  $\frac { 8 } { 11 }$

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport. -During which hour did the temperature increase the most?

For the given functions f and g , find the indicated composition. - $f(x)=4 x+15, \quad g(x)=4 x-1$ $(f \circ g)(x)$

Describe how the graph of the equation relates to the graph of y $y = x ^ { 2 }$ - $f ( x ) = ( x - 5 ) ^ { 2 } + 9$

Find the average rate of change illustrated in the graph. - Usage (in minutes)

Determine whether the three points are the vertices of a right triangle. -(5, 6), (7, 10), (9, 9)

For the given functions f and g , find the indicated composition. - $f ( x ) = 4 x ^ { 2 } + 5 x + 7 , \quad g ( x ) = 5 x - 6$

Find the average rate of change illustrated in the graph. -The linear function $f ( x ) = 1.8 x + 22$ models the percentage of people, $f ( x )$ , who graduated from college $x$ years after 1998. Find and interpret the slope.

Describe how the graph of the equation relates to the graph of y $y = x ^ { 2 }$ - $f ( x ) = \frac { 1 } { 5 } x ^ { 2 } - 3$

Graph the function. - $f(x)=2 \llbracket x \rrbracket$ $Graph the function. - f(x)=2 \llbracket x \rrbracket$

Graph the function. - $y=\sqrt{x-6}+7$ $Graph the function. - y=\sqrt{x-6}+7$

Find the specified domain. -The graphs of functions $f$ and $g$ are shown. Use these graphs to find $( f + g ) ( - 2 )$ .

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. - $y = 3 x ^ { 2 } + 4$

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

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

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

Determine if the function is even, odd, or neither. - $f ( x ) = - 8 x ^ { 3 } + 5 x ^ { 2 } - 2$

Find the center-radius form of the equation of the circle. -center $( 0,2 )$ , radius $\sqrt { 19 }$

Graph the function. - $f ( x ) = \frac { 1 } { 5 } \sqrt { - x }$ $Graph the function. - f ( x ) = \frac { 1 } { 5 } \sqrt { - x }$

Find the center-radius form of the circle described or graphed. -a circle having a diameter with endpoints $( - 2,8 )$ and $( 8,2 )$

Find the slope of the line satisfying the given conditions. -through $( - 6 , - 7 )$ and $( 5,1 )$

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

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport. -During which hour did the temperature increase the most?

For the given functions f and g , find the indicated composition. - f(x)=4x+15,g(x)=4x−1f(x)=4 x+15, \quad g(x)=4 x-1f(x)=4x+15,g(x)=4x−1 (f∘g)(x)(f \circ g)(x)(f∘g)(x)

Describe how the graph of the equation relates to the graph of y y=x2y = x ^ { 2 }y=x2 - f(x)=(x−5)2+9f ( x ) = ( x - 5 ) ^ { 2 } + 9f(x)=(x−5)2+9

Find the average rate of change illustrated in the graph. - Usage (in minutes)

Determine whether the three points are the vertices of a right triangle. -(5, 6), (7, 10), (9, 9)

For the given functions f and g , find the indicated composition. - f(x)=4x2+5x+7,g(x)=5x−6f ( x ) = 4 x ^ { 2 } + 5 x + 7 , \quad g ( x ) = 5 x - 6f(x)=4x2+5x+7,g(x)=5x−6

Find the average rate of change illustrated in the graph. -The linear function f(x)=1.8x+22f ( x ) = 1.8 x + 22f(x)=1.8x+22 models the percentage of people, f(x)f ( x )f(x) , who graduated from college xxx years after 1998. Find and interpret the slope.

Describe how the graph of the equation relates to the graph of y y=x2y = x ^ { 2 }y=x2 - f(x)=15x2−3f ( x ) = \frac { 1 } { 5 } x ^ { 2 } - 3f(x)=51​x2−3

Graph the function. - f(x)=2⟦x⟧f(x)=2 \llbracket x \rrbracketf(x)=2[[x]]

Graph the function. - y=x−6+7y=\sqrt{x-6}+7y=x−6​+7

Find the specified domain. -The graphs of functions fff and ggg are shown. Use these graphs to find (f+g)(−2)( f + g ) ( - 2 )(f+g)(−2) .

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=3x2+4y = 3 x ^ { 2 } + 4y=3x2+4

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

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

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

Determine if the function is even, odd, or neither. - f(x)=−8x3+5x2−2f ( x ) = - 8 x ^ { 3 } + 5 x ^ { 2 } - 2f(x)=−8x3+5x2−2

Find the center-radius form of the equation of the circle. -center (0,2)( 0,2 )(0,2) , radius 19\sqrt { 19 }19​

Graph the function. - f(x)=15−xf ( x ) = \frac { 1 } { 5 } \sqrt { - x }f(x)=51​−x​

Find the center-radius form of the circle described or graphed. -a circle having a diameter with endpoints (−2,8)( - 2,8 )(−2,8) and (8,2)( 8,2 )(8,2)

Find the slope of the line satisfying the given conditions. -through (−6,−7)( - 6 , - 7 )(−6,−7) and (5,1)( 5,1 )(5,1)

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

For the given functions f and g , find the indicated composition. - $f(x)=4 x+15, \quad g(x)=4 x-1$ $(f \circ g)(x)$

Describe how the graph of the equation relates to the graph of y $y = x ^ { 2 }$ - $f ( x ) = ( x - 5 ) ^ { 2 } + 9$

For the given functions f and g , find the indicated composition. - $f ( x ) = 4 x ^ { 2 } + 5 x + 7 , \quad g ( x ) = 5 x - 6$

Find the average rate of change illustrated in the graph. -The linear function $f ( x ) = 1.8 x + 22$ models the percentage of people, $f ( x )$ , who graduated from college $x$ years after 1998. Find and interpret the slope.

Describe how the graph of the equation relates to the graph of y $y = x ^ { 2 }$ - $f ( x ) = \frac { 1 } { 5 } x ^ { 2 } - 3$

Graph the function. - $f(x)=2 \llbracket x \rrbracket$ $Graph the function. - f(x)=2 \llbracket x \rrbracket$

Graph the function. - $y=\sqrt{x-6}+7$ $Graph the function. - y=\sqrt{x-6}+7$

Find the specified domain. -The graphs of functions $f$ and $g$ are shown. Use these graphs to find $( f + g ) ( - 2 )$ .

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. - $y = 3 x ^ { 2 } + 4$

Determine if the function is even, odd, or neither. - $f ( x ) = - 8 x ^ { 3 } + 5 x ^ { 2 } - 2$

Find the center-radius form of the equation of the circle. -center $( 0,2 )$ , radius $\sqrt { 19 }$

Graph the function. - $f ( x ) = \frac { 1 } { 5 } \sqrt { - x }$ $Graph the function. - f ( x ) = \frac { 1 } { 5 } \sqrt { - x }$

Find the center-radius form of the circle described or graphed. -a circle having a diameter with endpoints $( - 2,8 )$ and $( 8,2 )$

Find the slope of the line satisfying the given conditions. -through $( - 6 , - 7 )$ and $( 5,1 )$