Question 1

Match the numerical model to the corresponding model.
-

Accepted Answer

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

Question 2

Solve the equation graphically by converting it to an equivalent equation with 0 on the right-hand side and then finding
the x-intercepts.
-$4 x-20=x^{3}-9$

Accepted Answer

A)  $2.8$ 
B)  $- 29$ 
C)  $- 2.8 , - 29$ 
D)  $- 2.8$ 
A)  $2.8$ 
B)  $- 29$ 
C)  $- 2.8 , - 29$ 
D)  $- 2.8$

Question 3

Find f(x) and g(x) so that the function can be described as y = f(g(x)).
-$$y = ( 9 x - 16 ) ^ { 7 }$$

Accepted Answer

A)  $f ( x ) = x ^ { 7 } , g ( x ) = 9 x - 16$ 
B)  $f ( x ) = ( 9 x ) ^ { 7 } , g ( x ) = - 16$ 
C)  $f ( x ) = 9 x - 16 , g ( x ) = x ^ { 7 }$ 
D)  $f ( x ) = 9 x ^ { 7 } , g ( x ) = x - 16$ 
A)  $f ( x ) = x ^ { 7 } , g ( x ) = 9 x - 16$ 
B)  $f ( x ) = ( 9 x ) ^ { 7 } , g ( x ) = - 16$ 
C)  $f ( x ) = 9 x - 16 , g ( x ) = x ^ { 7 }$ 
D)  $f ( x ) = 9 x ^ { 7 } , g ( x ) = x - 16$

Question 4

Solve the problem.
-How many liters of a 30% alcohol solution must be mixed with 90 liters of a 80% solution to get a 60% solution?

Accepted Answer

A)  150 L 
B)  6 L 
C)  60 L 
D)  15 L 
A)  150 L 
B)  6 L 
C)  60 L 
D)  15 L

Question 5

Find the domain of the given function.
-$$f ( x ) = \frac { 5 } { x ^ { 2 } }$$

Accepted Answer

A)  $( - \infty , 3 ] \cup [ 3 , \infty )$ 
B)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  All real numbers 
D)  $[ 0 , \infty )$ 
A)  $( - \infty , 3 ] \cup [ 3 , \infty )$ 
B)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  All real numbers 
D)  $[ 0 , \infty )$

Question 6

Find the range of the function.
-$$f ( x ) = x ^ { 2 } + 1$$

Accepted Answer

A)  $[ 1 , \infty )$ 
B)  $( - 1 , \infty )$ 
C)  $( - \infty , 1 ]$ 
D)  $( - \infty , \infty )$ 
A)  $[ 1 , \infty )$ 
B)  $( - 1 , \infty )$ 
C)  $( - \infty , 1 ]$ 
D)  $( - \infty , \infty )$

Question 7

Find the inverse of the function.
-$$f ( x ) = x ^ { 3 } - 4$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } + 4$ 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 4 }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } - 4 }$ 
D)  Not a one-to-one function 
A)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } + 4$ 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 4 }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } - 4 }$ 
D)  Not a one-to-one function

Question 8

Solve the problem.
-The following information pertains to a bakery which makes donuts.

Make a scatterplot of the data. Based upon the scatterplot, what type of function would best model the data?

Accepted Answer

A)  Constant function 
B)  Quadratic function 
C)  Linear function 
D)  All of the above 
A)  Constant function 
B)  Quadratic function 
C)  Linear function 
D)  All of the above

Question 9

Sketch the graph of y1 as a solid line or curve. Then sketch the graph of y2 as a dashed line or curve by one or more of
these: a vertical and/or horizontal shift of the graph y1, a vertical stretch or shrink of the graph of y1, or a reflection of the
graph of y1 across an axis.
-$$y _ { 1 } = \sqrt [ 3 ] { x } , y _ { 2 } = \sqrt [ 3 ] { - x } + 3$$

Accepted Answer

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

Question 10

Match the numerical model to the corresponding model.
-$\begin{array}{c|rrrrrr}
x & 0 & 1 & 2 & 3 & 4 & 5 \
\hline y & 0 & 2 & 10 & 21 & 36 & 55
\end{array}$

Accepted Answer

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

Question 11

Determine whether the graph is the graph of a function.
-

Accepted Answer

A) True 
 B)False

Question 12

Solve the equation algebraically.
-$$v ^ { 2 } + 2 = 8 - 4 v ^ { 2 }$$

Accepted Answer

A)  $\pm \sqrt { \frac { 6 } { 5 } }$ 
B)  $\pm \sqrt { \frac { 1 } { 4 } }$ 
C)  $\pm \sqrt { \frac { 1 } { 2 } }$ 
D)  $\pm \sqrt { \frac { 5 } { 6 } }$ 
A)  $\pm \sqrt { \frac { 6 } { 5 } }$ 
B)  $\pm \sqrt { \frac { 1 } { 4 } }$ 
C)  $\pm \sqrt { \frac { 1 } { 2 } }$ 
D)  $\pm \sqrt { \frac { 5 } { 6 } }$

Question 13

Solve the problem.
-The following information pertains to a bakery which makes donuts.

Make a scatterplot of the data. Then graph the following four functions on the same coordinate system: $\mathrm { f } _ { 1 } ( \mathrm { x } ) = { } ^ { 4 }$ $\mathrm { f } _ { 2 } ( \mathrm { x } ) = 85 \mathrm { x } ; \mathrm { f } _ { 3 } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 100 \mathrm { x } ; \mathrm { f } _ { 4 } ( \mathrm { x } ) = 40 \mathrm { x } + 1000$. Which function best models the profit for $x$ cases of donuts?

Accepted Answer

A)  $\mathrm { f } _ { 4 }$ 
B)  $\mathrm { f } _ { 1 }$ 
C)  $\mathrm { f } _ { 2 }$ 
D)  $\mathrm { f } _ { 3 }$ 
A)  $\mathrm { f } _ { 4 }$ 
B)  $\mathrm { f } _ { 1 }$ 
C)  $\mathrm { f } _ { 2 }$ 
D)  $\mathrm { f } _ { 3 }$

Question 14

Perform the requested operation or operations.
-$f ( x ) = 4 x ^ { 2 } + 5 x + 4 ; g ( x ) = 5 x - 6$, find $g ( f ( x ) )$

Accepted Answer

A)  $g ( f ( x ) ) = 4 x ^ { 2 } + 5 x - 2$ 
B)  $g ( f ( x ) ) = 4 x ^ { 2 } + 25 x + 14$ 
C)  $g ( f ( x ) ) = 20 x ^ { 2 } + 25 x + 14$ 
D)  $g ( f ( x ) ) = 20 x ^ { 2 } + 25 x + 26$ 
A)  $g ( f ( x ) ) = 4 x ^ { 2 } + 5 x - 2$ 
B)  $g ( f ( x ) ) = 4 x ^ { 2 } + 25 x + 14$ 
C)  $g ( f ( x ) ) = 20 x ^ { 2 } + 25 x + 14$ 
D)  $g ( f ( x ) ) = 20 x ^ { 2 } + 25 x + 26$

Question 15

Graph the function on your calculator to determine the domain and range from the graph.
-$$r ( x ) = \sqrt { x + 6 }$$

Accepted Answer

A)  Domain: $[ - 6 , \infty )$; range: $[ 0 , \infty )$ 
B)  Domain: $[ - 6 , \infty )$; range: $( - \infty , \infty )$ 
C)  Domain: $[ 0 , \infty )$; range: $[ - 6 , \infty )$ 
D)  Domain: $( - 6 , \infty )$; range: $( 0 , \infty )$ 
A)  Domain: $[ - 6 , \infty )$; range: $[ 0 , \infty )$ 
B)  Domain: $[ - 6 , \infty )$; range: $( - \infty , \infty )$ 
C)  Domain: $[ 0 , \infty )$; range: $[ - 6 , \infty )$ 
D)  Domain: $( - 6 , \infty )$; range: $( 0 , \infty )$

Question 16

Determine algebraically whether the function is even, odd, or neither even nor odd.
-$$f ( x ) = - 5 x ^ { 3 } + 3 x$$

Accepted Answer

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

Question 17

Choose the one alternative that best completes the statement or answers the question.
Graph the piecewise-defined function.
-$$f ( x ) = \left\{ \begin{array} { l } 
| x | - 4 , \text { if } x < 0 \
- 4 , \text { if } x \geq 0
\end{array} \right.$$

Accepted Answer

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

Question 18

Choose the one alternative that best completes the statement or answers the question.
Write a mathematical expression for the quantity described verbally.
-The revenue when each item sells for $\$ 31,416$.

Accepted Answer

A)  $31,416 - x$ 
B)  $31,416 + x$ 
C)  $31,416 x$ 
D)  $x - 31,416$ 
A)  $31,416 - x$ 
B)  $31,416 + x$ 
C)  $31,416 x$ 
D)  $x - 31,416$

Question 19

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-$$y = ( x + 9 ) ^ { 2 } - 15$$

Accepted Answer

A)  Shift the graph of $y = x ^ { 2 }$ down 9 units and then left 15 units. 
B)  Shift the graph of $y = x ^ { 2 }$ right 9 units and then down 15 units. 
C)  Shift the graph of $y = x ^ { 2 }$ up 9 units and then right 15 units. 
D)  Shift the graph of $y = x ^ { 2 }$ left 9 units and then down 15 units. 
A)  Shift the graph of $y = x ^ { 2 }$ down 9 units and then left 15 units. 
B)  Shift the graph of $y = x ^ { 2 }$ right 9 units and then down 15 units. 
C)  Shift the graph of $y = x ^ { 2 }$ up 9 units and then right 15 units. 
D)  Shift the graph of $y = x ^ { 2 }$ left 9 units and then down 15 units.

Question 20

Graph the function and determine if it has a point of discontinuity at x = 0. If there is a discontinuity, tell whether it is
removable or non-removable.
-$$f ( x ) = \frac { | x + 4 | } { x }$$

Accepted Answer

A) 
 
No 
B) 
 
No 
C) 
 
Yes; removable 
D) 
 
Yes; non-removable 
A) 
 
No 
B) 
 
No 
C) 
 
Yes; removable 
D) 
 
Yes; non-removable

Match the numerical model to the corresponding model. -

Find f(x) and g(x) so that the function can be described as y = f(g(x)). - $y = ( 9 x - 16 ) ^ { 7 }$

Solve the problem. -How many liters of a 30% alcohol solution must be mixed with 90 liters of a 80% solution to get a 60% solution?

Find the domain of the given function. - $f ( x ) = \frac { 5 } { x ^ { 2 } }$

Find the range of the function. - $f ( x ) = x ^ { 2 } + 1$

Find the inverse of the function. - $f ( x ) = x ^ { 3 } - 4$

Solve the problem. -The following information pertains to a bakery which makes donuts. Make a scatterplot of the data. Based upon the scatterplot, what type of function would best model the data?

Match the numerical model to the corresponding model. - x 0 1 2 3 4 5 y 0 2 10 21 36 55

Determine whether the graph is the graph of a function. -

Solve the equation algebraically. - $v ^ { 2 } + 2 = 8 - 4 v ^ { 2 }$

Perform the requested operation or operations. - $f ( x ) = 4 x ^ { 2 } + 5 x + 4 ; g ( x ) = 5 x - 6$ , find $g ( f ( x ) )$

Graph the function on your calculator to determine the domain and range from the graph. - $r ( x ) = \sqrt { x + 6 }$

Determine algebraically whether the function is even, odd, or neither even nor odd. - $f ( x ) = - 5 x ^ { 3 } + 3 x$

Choose the one alternative that best completes the statement or answers the question. Write a mathematical expression for the quantity described verbally. -The revenue when each item sells for $\$ 31,416$ .

Choose the one alternative that best completes the statement or answers the question. Solve the problem. - $y = ( x + 9 ) ^ { 2 } - 15$

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 1: Functions and Graphs

Match the numerical model to the corresponding model. -

Solve the equation graphically by converting it to an equivalent equation with 0 on the right-hand side and then finding the x-intercepts. - 4x−20=x3−94 x-20=x^{3}-94x−20=x3−9

Find f(x) and g(x) so that the function can be described as y = f(g(x)). - y=(9x−16)7y = ( 9 x - 16 ) ^ { 7 }y=(9x−16)7

Solve the problem. -How many liters of a 30% alcohol solution must be mixed with 90 liters of a 80% solution to get a 60% solution?

Find the domain of the given function. - f(x)=5x2f ( x ) = \frac { 5 } { x ^ { 2 } }f(x)=x25​

Find the range of the function. - f(x)=x2+1f ( x ) = x ^ { 2 } + 1f(x)=x2+1

Find the inverse of the function. - f(x)=x3−4f ( x ) = x ^ { 3 } - 4f(x)=x3−4

Solve the problem. -The following information pertains to a bakery which makes donuts. Make a scatterplot of the data. Based upon the scatterplot, what type of function would best model the data?

Match the numerical model to the corresponding model. - x 0 1 2 3 4 5 y 0 2 10 21 36 55

Determine whether the graph is the graph of a function. -

Solve the equation algebraically. - v2+2=8−4v2v ^ { 2 } + 2 = 8 - 4 v ^ { 2 }v2+2=8−4v2

Perform the requested operation or operations. - f(x)=4x2+5x+4;g(x)=5x−6f ( x ) = 4 x ^ { 2 } + 5 x + 4 ; g ( x ) = 5 x - 6f(x)=4x2+5x+4;g(x)=5x−6 , find g(f(x))g ( f ( x ) )g(f(x))

Graph the function on your calculator to determine the domain and range from the graph. - r(x)=x+6r ( x ) = \sqrt { x + 6 }r(x)=x+6​

Determine algebraically whether the function is even, odd, or neither even nor odd. - f(x)=−5x3+3xf ( x ) = - 5 x ^ { 3 } + 3 xf(x)=−5x3+3x

Choose the one alternative that best completes the statement or answers the question. Write a mathematical expression for the quantity described verbally. -The revenue when each item sells for $31,416\$ 31,416$31,416 .

Choose the one alternative that best completes the statement or answers the question. Solve the problem. - y=(x+9)2−15y = ( x + 9 ) ^ { 2 } - 15y=(x+9)2−15

Graph the function and determine if it has a point of discontinuity at x = 0. If there is a discontinuity, tell whether it is removable or non-removable. - f(x)=∣x+4∣xf ( x ) = \frac { | x + 4 | } { x }f(x)=x∣x+4∣​

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Find f(x) and g(x) so that the function can be described as y = f(g(x)). - $y = ( 9 x - 16 ) ^ { 7 }$

Find the domain of the given function. - $f ( x ) = \frac { 5 } { x ^ { 2 } }$

Find the range of the function. - $f ( x ) = x ^ { 2 } + 1$

Find the inverse of the function. - $f ( x ) = x ^ { 3 } - 4$

Solve the equation algebraically. - $v ^ { 2 } + 2 = 8 - 4 v ^ { 2 }$

Perform the requested operation or operations. - $f ( x ) = 4 x ^ { 2 } + 5 x + 4 ; g ( x ) = 5 x - 6$ , find $g ( f ( x ) )$

Graph the function on your calculator to determine the domain and range from the graph. - $r ( x ) = \sqrt { x + 6 }$

Determine algebraically whether the function is even, odd, or neither even nor odd. - $f ( x ) = - 5 x ^ { 3 } + 3 x$

Choose the one alternative that best completes the statement or answers the question. Write a mathematical expression for the quantity described verbally. -The revenue when each item sells for $\$ 31,416$ .

Choose the one alternative that best completes the statement or answers the question. Solve the problem. - $y = ( x + 9 ) ^ { 2 } - 15$