Question 1

Write an equation for the line described. Give your answer in slope-intercept form.
-$\mathrm { m } = - 7$, through $( - 4,2 )$

Accepted Answer

A)  $y = 7 x - 24$ 
B)  $y = - 7 x - 26$ 
C)  $y = - 7 x + 33$ 
D)  $7 x + y = 26$ 
A)  $y = 7 x - 24$ 
B)  $y = - 7 x - 26$ 
C)  $y = - 7 x + 33$ 
D)  $7 x + y = 26$

Question 2

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

Accepted Answer

A)  $f ( x ) = \left\{ \begin{array} { l l } x ^ { 3 } & \text { if } x < 1 \ x + 4 & \text { if } x \geq 1 \end{array} ; \right.$ Domain: $( \infty , \infty )$, Range: $( \infty , 1 ) \cup [ 5 , \infty )$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } x ^ { 3 } & \text { if } x < 1 \ x - 4 & \text { if } x \geq 1 \end{array} ; \right.$ Domain: $( \infty , 1 ) \cup [ 5 , \infty )$, Range: $( \infty , \infty )$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } \sqrt [ 3 ] { x } & \text { if } x < 1 ; \text { Domain: } ( \infty , \infty ) , \text { Range: } ( \infty , 1 ) \cup [ 5 , \infty ) \ x + 4 & \text { if } x \geq 1 \end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } - x ^ { 3 } & \text { if } x < 1 \ x - 4 & \text { if } x \geq 1 \end{array} ; \right.$ Domain: $( \infty , 1 ) \cup [ 5 , \infty )$, Range: $( \infty , \infty )$ 
A)  $f ( x ) = \left\{ \begin{array} { l l } x ^ { 3 } & \text { if } x < 1 \ x + 4 & \text { if } x \geq 1 \end{array} ; \right.$ Domain: $( \infty , \infty )$, Range: $( \infty , 1 ) \cup [ 5 , \infty )$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } x ^ { 3 } & \text { if } x < 1 \ x - 4 & \text { if } x \geq 1 \end{array} ; \right.$ Domain: $( \infty , 1 ) \cup [ 5 , \infty )$, Range: $( \infty , \infty )$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } \sqrt [ 3 ] { x } & \text { if } x < 1 ; \text { Domain: } ( \infty , \infty ) , \text { Range: } ( \infty , 1 ) \cup [ 5 , \infty ) \ x + 4 & \text { if } x \geq 1 \end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } - x ^ { 3 } & \text { if } x < 1 \ x - 4 & \text { if } x \geq 1 \end{array} ; \right.$ Domain: $( \infty , 1 ) \cup [ 5 , \infty )$, Range: $( \infty , \infty )$

Question 3

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ .
-$f(x)=-(x-6)^{2}-2$

Accepted Answer

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

Question 4

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

Question 5

Give the domain and range of the relation.
-Find $g ( a + 1 )$ when $g ( x ) = 4 x + 3$

Accepted Answer

A)  $4 a + 7$ 
B)  $4 a - 1$ 
C)  $4 a + 3$ 
D)  $\frac { 1 } { 4 } a + 3$ 
A)  $4 a + 7$ 
B)  $4 a - 1$ 
C)  $4 a + 3$ 
D)  $\frac { 1 } { 4 } a + 3$

Question 6

Find the slope of the line and sketch the graph.
-$$2 x - 3 y = - 3$$

Accepted Answer

A)  $\mathrm { m } = \frac { 2 } { 3 }$
  
B)  $m = - \frac { 3 } { 2 }$
  
C)  $m = - \frac { 2 } { 3 }$
  
D)  $m = \frac { 3 } { 2 }$
  
A)  $\mathrm { m } = \frac { 2 } { 3 }$
  
B)  $m = - \frac { 3 } { 2 }$
  
C)  $m = - \frac { 2 } { 3 }$
  
D)  $m = \frac { 3 } { 2 }$

Question 7

Graph the line and give the domain and the range.
-$y+4=0$

Accepted Answer

A)  $D = ( - \infty , \infty ) , R = \{ - 4 \}$
  
B)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = \{ - 4 \}$
  
C)  $\mathrm { D } = \{ - 4 \} , \quad R = ( - \infty , \infty )$
  
D)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
A)  $D = ( - \infty , \infty ) , R = \{ - 4 \}$
  
B)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = \{ - 4 \}$
  
C)  $\mathrm { D } = \{ - 4 \} , \quad R = ( - \infty , \infty )$
  
D)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$

Question 8

Determine the intervals of the domain over which the function is continuous.
-P(2, 3)

Accepted Answer

A)  $( - \infty , 2 ] \cup [ 2 , \infty )$ 
B)  $( - \infty , 3 ) \cup ( 3 , \infty )$ 
C)  $( - \infty , 2 ) \cup ( 2 , \infty )$ 
D)  $( - \infty , \infty )$ 
A)  $( - \infty , 2 ] \cup [ 2 , \infty )$ 
B)  $( - \infty , 3 ) \cup ( 3 , \infty )$ 
C)  $( - \infty , 2 ) \cup ( 2 , \infty )$ 
D)  $( - \infty , \infty )$

Question 9

For the pair of functions, find the indicated sum, difference, product, or quotient.
-$$f ( x ) = \sqrt { 3 x + 5 } , g ( x ) = \sqrt { 9 x - 16 }$$
Find $( f g ) ( x )$.

Accepted Answer

A)  $( \sqrt { 3 x + 5 } ) ( \sqrt { 9 x - 16 } )$ 
B)  $( 3 x + 5 ) ( 9 x - 16 )$ 
C)  $( 3 x + 5 ) ( 3 x - 4 )$ 
D)  $( 3 x - 4 ) ( \sqrt { 3 x + 5 } )$ 
A)  $( \sqrt { 3 x + 5 } ) ( \sqrt { 9 x - 16 } )$ 
B)  $( 3 x + 5 ) ( 9 x - 16 )$ 
C)  $( 3 x + 5 ) ( 3 x - 4 )$ 
D)  $( 3 x - 4 ) ( \sqrt { 3 x + 5 } )$

Question 10

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-midpoint $( - 8 , - 9 )$, endpoint $( - 10 , - 5 )$

Accepted Answer

A)  $( - 6 , - 13 )$ 
B)  $( - 6 , - 1 )$ 
C)  $( - 18 , - 1 )$ 
D)  $( - 14,3 )$ 
A)  $( - 6 , - 13 )$ 
B)  $( - 6 , - 1 )$ 
C)  $( - 18 , - 1 )$ 
D)  $( - 14,3 )$

Question 11

Graph the equation by plotting points.
-$y=(x+1)^{3}$

Accepted Answer

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

Question 12

Graph the point symmetric to the given point.
-$$\text { Plot the point } ( - 4,7 ) \text {, then plot the point that is symmetric to } ( - 4,7 ) \text { with respect to the } y \text {-axis. }$$

Accepted Answer

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

Question 13

Decide whether the relation defines a function.
-$y = \frac { 3 } { x - 3 }$

Accepted Answer

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

Question 14

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ .
-$$f ( x ) = \frac { 1 } { 3 } | - x |$$

Accepted Answer

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

Question 15

Determine whether the three points are collinear.
-Which graphs of functions increase over the whole of their domain?

Accepted Answer

A)  graphs A and B 
B)  graphs C and D 
C)  graphs A and D 
D)  graph D 
A)  graphs A and B 
B)  graphs C and D 
C)  graphs A and D 
D)  graph D

Question 16

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such.
-$f(x)=\frac{1}{4} x+6$

Accepted Answer

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

Question 17

Find the specified domain.
-Find the domain of $( f + g ) ( x )$ when $f ( x ) = 3 x + 9$ and $g ( x ) = \frac { 2 } { x - 8 }$

Accepted Answer

A)  $( - \infty , 8 ) \cup ( 8 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
D)  $( - \infty , - 8 ) \cup ( - 8 , \infty )$ 
A)  $( - \infty , 8 ) \cup ( 8 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
D)  $( - \infty , - 8 ) \cup ( - 8 , \infty )$

Question 18

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$
-$$f ( x ) = 2 x ^ { 2 } + 7 x$$

Accepted Answer

A)  $6 x - 4 h + 14$ 
B)  $4 x ^ { 2 } + 2 h + 7 x$ 
C)  $4 x + 7$ 
D)  $4 x + 2 h + 7$ 
A)  $6 x - 4 h + 14$ 
B)  $4 x ^ { 2 } + 2 h + 7 x$ 
C)  $4 x + 7$ 
D)  $4 x + 2 h + 7$

Question 19

Find the center and radius of the circle.
-$$x ^ { 2 } + y ^ { 2 } + 4 x - 16 y - 13 = 0$$

Accepted Answer

A)  center: $( 2 , - 8 )$; radius: 81 
B)  center: $( - 2,8 )$; radius: 9 
C)  center: $( - 8,2 )$; radius: 81 
D)  center: $( 8 , - 2 )$; radius: 9 
A)  center: $( 2 , - 8 )$; radius: 81 
B)  center: $( - 2,8 )$; radius: 9 
C)  center: $( - 8,2 )$; radius: 81 
D)  center: $( 8 , - 2 )$; radius: 9

Question 20

A new chocolate company is estimating how many candy bars per week college students will consume of their line of
products. The graph shows the probable number of candy bars students (age 18-22) will consume from year 0 to year 10.
B(x) gives the number of candy bars for boys, G(x) gives the number of candy bars for girls, and T(x) gives the total
number for both groups. Use the graph to answer the question.  
-The radius $\mathrm { r }$ of a circle of known area $\mathrm { A }$ is given by $\mathrm { r } = \sqrt { \mathrm { A } / \pi }$, where $\pi \approx 3.1416$. Find the radius and circumference of a circle with an area of $48.71 \mathrm { sq } \mathrm { ft }$. (Round results to two decimal places.)

Accepted Answer

A)  $\mathrm { r } = 15.52 \mathrm { ft } , \mathrm { C } = 97.52 \mathrm { ft }$ 
B)  $\mathrm { r } = 3.94 \mathrm { ft } , \mathrm { C } = 24.76 \mathrm { ft }$ 
C)  $\mathrm { r } = 3.94 \mathrm { ft } , \mathrm { C } = 24.76 \mathrm { sq } \mathrm { ft }$ 
D)  $\mathrm { r } = 3.94 \mathrm { ft } , \mathrm { C } = 8.86 \mathrm { ft }$ 
A)  $\mathrm { r } = 15.52 \mathrm { ft } , \mathrm { C } = 97.52 \mathrm { ft }$ 
B)  $\mathrm { r } = 3.94 \mathrm { ft } , \mathrm { C } = 24.76 \mathrm { ft }$ 
C)  $\mathrm { r } = 3.94 \mathrm { ft } , \mathrm { C } = 24.76 \mathrm { sq } \mathrm { ft }$ 
D)  $\mathrm { r } = 3.94 \mathrm { ft } , \mathrm { C } = 8.86 \mathrm { ft }$

Write an equation for the line described. Give your answer in slope-intercept form. - $\mathrm { m } = - 7$ , through $( - 4,2 )$

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

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ . - $f(x)=-(x-6)^{2}-2$ $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } . - f(x)=-(x-6)^{2}-2$

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

Give the domain and range of the relation. -Find $g ( a + 1 )$ when $g ( x ) = 4 x + 3$

Find the slope of the line and sketch the graph. - $2 x - 3 y = - 3$

Graph the line and give the domain and the range. - $y+4=0$

Determine the intervals of the domain over which the function is continuous. -P(2, 3)

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = \sqrt { 3 x + 5 } , g ( x ) = \sqrt { 9 x - 16 }$ Find $( f g ) ( x )$ .

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint $( - 8 , - 9 )$ , endpoint $( - 10 , - 5 )$

Graph the equation by plotting points. - $y=(x+1)^{3}$ $Graph the equation by plotting points. - y=(x+1)^{3}$

Decide whether the relation defines a function. - $y = \frac { 3 } { x - 3 }$

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ . - $f ( x ) = \frac { 1 } { 3 } | - x |$ $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } . - f ( x ) = \frac { 1 } { 3 } | - x |$

Determine whether the three points are collinear. -Which graphs of functions increase over the whole of their domain?

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - $f(x)=\frac{1}{4} x+6$ $Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - f(x)=\frac{1}{4} x+6$

Find the specified domain. -Find the domain of $( f + g ) ( x )$ when $f ( x ) = 3 x + 9$ and $g ( x ) = \frac { 2 } { x - 8 }$

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$ - $f ( x ) = 2 x ^ { 2 } + 7 x$

Find the center and radius of the circle. - $x ^ { 2 } + y ^ { 2 } + 4 x - 16 y - 13 = 0$

Review of Basic Concepts

Equations and Inequalities

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 3: Graphs and Functions

Write an equation for the line described. Give your answer in slope-intercept form. - m=−7\mathrm { m } = - 7m=−7 , through (−4,2)( - 4,2 )(−4,2)

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

Describe how the graph of the equation relates to the graph of y y=x3y = \sqrt [ 3 ] { x }y=3x​ . - f(x)=−(x−6)2−2f(x)=-(x-6)^{2}-2f(x)=−(x−6)2−2

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - f(x)=14xf(x)=\frac{1}{4} xf(x)=41​x

Give the domain and range of the relation. -Find g(a+1)g ( a + 1 )g(a+1) when g(x)=4x+3g ( x ) = 4 x + 3g(x)=4x+3

Find the slope of the line and sketch the graph. - 2x−3y=−32 x - 3 y = - 32x−3y=−3

Graph the line and give the domain and the range. - y+4=0y+4=0y+4=0

Determine the intervals of the domain over which the function is continuous. -P(2, 3)

For the pair of functions, find the indicated sum, difference, product, or quotient. - f(x)=3x+5,g(x)=9x−16f ( x ) = \sqrt { 3 x + 5 } , g ( x ) = \sqrt { 9 x - 16 }f(x)=3x+5​,g(x)=9x−16​ Find (fg)(x)( f g ) ( x )(fg)(x) .

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint (−8,−9)( - 8 , - 9 )(−8,−9) , endpoint (−10,−5)( - 10 , - 5 )(−10,−5)

Graph the equation by plotting points. - y=(x+1)3y=(x+1)^{3}y=(x+1)3

Decide whether the relation defines a function. - y=3x−3y = \frac { 3 } { x - 3 }y=x−33​

Describe how the graph of the equation relates to the graph of y y=x3y = \sqrt [ 3 ] { x }y=3x​ . - f(x)=13∣−x∣f ( x ) = \frac { 1 } { 3 } | - x |f(x)=31​∣−x∣

Determine whether the three points are collinear. -Which graphs of functions increase over the whole of their domain?

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - f(x)=14x+6f(x)=\frac{1}{4} x+6f(x)=41​x+6

Find the specified domain. -Find the domain of (f+g)(x)( f + g ) ( x )(f+g)(x) when f(x)=3x+9f ( x ) = 3 x + 9f(x)=3x+9 and g(x)=2x−8g ( x ) = \frac { 2 } { x - 8 }g(x)=x−82​

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)=2x2+7xf ( x ) = 2 x ^ { 2 } + 7 xf(x)=2x2+7x

Find the center and radius of the circle. - x2+y2+4x−16y−13=0x ^ { 2 } + y ^ { 2 } + 4 x - 16 y - 13 = 0x2+y2+4x−16y−13=0

Review of Basic Concepts

Equations and Inequalities

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Write an equation for the line described. Give your answer in slope-intercept form. - $\mathrm { m } = - 7$ , through $( - 4,2 )$

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ . - $f(x)=-(x-6)^{2}-2$ $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } . - f(x)=-(x-6)^{2}-2$

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

Give the domain and range of the relation. -Find $g ( a + 1 )$ when $g ( x ) = 4 x + 3$

Find the slope of the line and sketch the graph. - $2 x - 3 y = - 3$

Graph the line and give the domain and the range. - $y+4=0$

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = \sqrt { 3 x + 5 } , g ( x ) = \sqrt { 9 x - 16 }$ Find $( f g ) ( x )$ .

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint $( - 8 , - 9 )$ , endpoint $( - 10 , - 5 )$

Graph the equation by plotting points. - $y=(x+1)^{3}$ $Graph the equation by plotting points. - y=(x+1)^{3}$

Decide whether the relation defines a function. - $y = \frac { 3 } { x - 3 }$

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ . - $f ( x ) = \frac { 1 } { 3 } | - x |$ $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } . - f ( x ) = \frac { 1 } { 3 } | - x |$

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - $f(x)=\frac{1}{4} x+6$ $Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - f(x)=\frac{1}{4} x+6$

Find the specified domain. -Find the domain of $( f + g ) ( x )$ when $f ( x ) = 3 x + 9$ and $g ( x ) = \frac { 2 } { x - 8 }$

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$ - $f ( x ) = 2 x ^ { 2 } + 7 x$

Find the center and radius of the circle. - $x ^ { 2 } + y ^ { 2 } + 4 x - 16 y - 13 = 0$