Question 1

Find an equation of the secant line containing (1, f(1)) and (2, f(2)).
-$$f ( x ) = \frac { 4 } { x + 3 }$$

Accepted Answer

A)  $y = \frac { 1 } { 5 } x + \frac { 4 } { 5 }$ 
B)  $y = \frac { 4 } { 5 } x + \frac { 1 } { 5 }$ 
C)  $y = - \frac { 1 } { 5 } x + \frac { 6 } { 5 }$ 
D)  $y = \frac { 1 } { 5 } x + \frac { 3 } { 2 }$ 
A)  $y = \frac { 1 } { 5 } x + \frac { 4 } { 5 }$ 
B)  $y = \frac { 4 } { 5 } x + \frac { 1 } { 5 }$ 
C)  $y = - \frac { 1 } { 5 } x + \frac { 6 } { 5 }$ 
D)  $y = \frac { 1 } { 5 } x + \frac { 3 } { 2 }$

Question 2

Answer the question about the given function.
-Given the function $f ( x ) = \frac { x ^ { 2 } + 8 } { x - 4 }$, list the $y$-intercept, if there is one, of the graph of $f$.

Accepted Answer

A)  $( 0,4 )$ 
B)  $( 0 , - 2 )$ 
C)  $( 0 , - 8 )$ 
D)  $( - 2,0 )$ 
A)  $( 0,4 )$ 
B)  $( 0 , - 2 )$ 
C)  $( 0 , - 8 )$ 
D)  $( - 2,0 )$

Question 3

Determine whether the equation defines y as a function of x.
-$$\mathrm { y } = \frac { 1 } { \mathrm { x } }$$

Accepted Answer

A)  function 
B)  not a function 
A)  function 
B)  not a function

Question 4

Choose the one alternative that best completes the statement or answers the question.
-The price $p$ and the quantity $x$ sold of a certain product obey the demand equation:
$$p = - \frac { 1 } { 5 } x + 200 , \{ x \mid 0 \leq x \leq 500 \}$$
What is the revenue to the nearest dollar when 300 units are sold?

Accepted Answer

A)  $\$ 110,000$ 
B)  $\$ 78,000$ 
C)  $\$ 20,000$ 
D)  $\$ 42,000$ 
A)  $\$ 110,000$ 
B)  $\$ 78,000$ 
C)  $\$ 20,000$ 
D)  $\$ 42,000$

Question 5

Choose the one alternative that best completes the statement or answers the question.
Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$f(x)=(x+7)^{2}+4$

Accepted Answer

A)

B) 
  
C) 
  
D) 
  
A)

B) 
  
C) 
  
D)

Question 6

Choose the one alternative that best completes the statement or answers the question.
-A farmer's silo is the shape of a cylinder with a hemisphere as the roof. If the radius of the hemisphere is 10 feet and the height of the silo is heet, express the volume of the silo as a function of h.

Accepted Answer

A)  $V ( h ) = 100 \pi ( h - 10 ) + \frac { 2000 } { 3 } \pi$ 
B)  $\mathrm { V } ( \mathrm { h } ) = 4100 \pi ( \mathrm { h } - 10 ) + \frac { 500 } { 7 } \pi$ 
C) $ \mathrm { V } ( \mathrm { h } ) = 100 \pi \mathrm { h } + \frac { 4000 } { 3 } \pi \mathrm { h } ^ { 2 }$ 
D)  $V ( h ) = 100 \pi \left( h ^ { 2 } - 10 \right) + \frac { 5000 } { 3 } \pi$ 
A)  $V ( h ) = 100 \pi ( h - 10 ) + \frac { 2000 } { 3 } \pi$ 
B)  $\mathrm { V } ( \mathrm { h } ) = 4100 \pi ( \mathrm { h } - 10 ) + \frac { 500 } { 7 } \pi$ 
C) $ \mathrm { V } ( \mathrm { h } ) = 100 \pi \mathrm { h } + \frac { 4000 } { 3 } \pi \mathrm { h } ^ { 2 }$ 
D)  $V ( h ) = 100 \pi \left( h ^ { 2 } - 10 \right) + \frac { 5000 } { 3 } \pi$

Question 7

The graph of a function f is given. Use the graph to answer the question.
-How often does the line y = 20 intersect the graph?

Accepted Answer

A)  once 
B)  twice 
C)  three times 
D)  does not intersect 
A)  once 
B)  twice 
C)  three times 
D)  does not intersect

Question 8

Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$f(x)=-2(x+1)^{2}-3$

Accepted Answer

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

Question 9

Choose the one alternative that best completes the statement or answers the question.
Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$f(x)=(x+2)^{3}$

Accepted Answer

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

Question 10

Solve the problem.
-If $f ( x ) = 9 x ^ { 3 } + 5 x ^ { 2 } - x + C$ and $f ( - 2 ) = 1$, what is the value of $C$ ?

Accepted Answer

A)  $C = - 53$ 
B)  $C = - 13$ 
C)  $C = 51$ 
D)  $C = - 93$ 
A)  $C = - 53$ 
B)  $C = - 13$ 
C)  $C = 51$ 
D)  $C = - 93$

Question 11

Answer the question about the given function.
-Given the function $f ( x ) = \frac { x ^ { 2 } + 3 } { x - 8 }$, what is the domain of $f$ ?

Accepted Answer

A)  $\{ x \mid x \neq - 8 \}$ 
B)  $\{ x \mid x \neq 3 \}$ 
C)  $\left\{ x \mid x \neq \frac { 3 } { 8 } \right\}$ 
D)  $\{ x \mid x \neq 8 \}$ 
A)  $\{ x \mid x \neq - 8 \}$ 
B)  $\{ x \mid x \neq 3 \}$ 
C)  $\left\{ x \mid x \neq \frac { 3 } { 8 } \right\}$ 
D)  $\{ x \mid x \neq 8 \}$

Question 12

Solve the problem.
-Suppose that P(x) represents the percentage of income spent on food in year x and I(x) represents income in year x. Determine a function F that represents total food expenditures in year x.

Accepted Answer

A)  $F ( x ) = ( P + I ) ( x )$ 
B)  $F ( x ) = ( P \cdot I ) ( x )$ 
C)  $F ( x ) = ( I - P ) ( x )$ 
D)  $F ( x ) = \left( \frac { I } { P } \right) ( x )$ 
A)  $F ( x ) = ( P + I ) ( x )$ 
B)  $F ( x ) = ( P \cdot I ) ( x )$ 
C)  $F ( x ) = ( I - P ) ( x )$ 
D)  $F ( x ) = \left( \frac { I } { P } \right) ( x )$

Question 13

For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists.
-

Accepted Answer

A)  Absolute maximum: $\mathrm { f } ( 3 ) = 6$; Absolute minimum: $\mathrm { f } ( 5 ) = 1$ 
B)  Absolute maximum: $\mathrm { f } ( 7 ) = 4$; Absolute minimum: $\mathrm { f } ( 0 ) = 2$ 
C)  Absolute maximum: $f ( 3 ) = 6$; Absolute minimum: none 
D)  Absolute maximum: $f ( 3 ) = 6$; Absolute minimum: $f ( 0 ) = 2$ 
A)  Absolute maximum: $\mathrm { f } ( 3 ) = 6$; Absolute minimum: $\mathrm { f } ( 5 ) = 1$ 
B)  Absolute maximum: $\mathrm { f } ( 7 ) = 4$; Absolute minimum: $\mathrm { f } ( 0 ) = 2$ 
C)  Absolute maximum: $f ( 3 ) = 6$; Absolute minimum: none 
D)  Absolute maximum: $f ( 3 ) = 6$; Absolute minimum: $f ( 0 ) = 2$

Question 14

For the given functions f and g, find the requested function and state its domain.
-$$f ( x ) = 7 x + 3 ; g ( x ) = 3 x + 7$$
Find $f \cdot g$.

Accepted Answer

A)  $( f \cdot g ) ( x ) = 21 x ^ { 2 } + 21 ; \{ x \mid x \neq 21 \}$ 
B)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 21 \mathrm { x } ^ { 2 } + 58 \mathrm { x } + 21$; all real numbers 
C)  $( f \cdot g ) ( x ) = 10 x ^ { 2 } + 58 x + 10$; all real numbers 
D)  $( f \cdot g ) ( x ) = 21 x ^ { 2 } + 16 x + 21 ; \{ x \mid x \neq 21 \}$ 
A)  $( f \cdot g ) ( x ) = 21 x ^ { 2 } + 21 ; \{ x \mid x \neq 21 \}$ 
B)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 21 \mathrm { x } ^ { 2 } + 58 \mathrm { x } + 21$; all real numbers 
C)  $( f \cdot g ) ( x ) = 10 x ^ { 2 } + 58 x + 10$; all real numbers 
D)  $( f \cdot g ) ( x ) = 21 x ^ { 2 } + 16 x + 21 ; \{ x \mid x \neq 21 \}$

Question 15

The graph of a piecewise-defined function is given. Write a definition for the function.
-

Accepted Answer

A) 
$f ( x ) = \left\{ \begin{array} { l l } \frac { 4 } { 3 } x - 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 2 } { 3 } x & \text { if } 0 \leq x \leq 3 \end{array} \right.$ 
B) 
$f ( x ) = \left\{ \begin{array} { l l } \frac { 3 } { 4 } x + 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 3 } { 2 } x & \text { if } 0 < x \leq 3 \end{array} \right.$ 
C) 
$f ( x ) = \left\{ \begin{array} { l l } 
\frac { 4 } { 3 } x + 4 & \text { if } - 3 \leq x \leq 0 \
\frac { 2 } { 3 } x + 2 & \text { if } 0 < x \leq 3
\end{array} \right.$ 
D) 
$f ( x ) = \left\{ \begin{array} { l l } 
\frac { 4 } { 3 } x + 4 & \text { if } - 3 \leq x \leq 0 \
\frac { 2 } { 3 } x & \text { if } 0 < x \leq 3
\end{array} \right.$ 
A) 
$f ( x ) = \left\{ \begin{array} { l l } \frac { 4 } { 3 } x - 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 2 } { 3 } x & \text { if } 0 \leq x \leq 3 \end{array} \right.$ 
B) 
$f ( x ) = \left\{ \begin{array} { l l } \frac { 3 } { 4 } x + 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 3 } { 2 } x & \text { if } 0 < x \leq 3 \end{array} \right.$ 
C) 
$f ( x ) = \left\{ \begin{array} { l l } 
\frac { 4 } { 3 } x + 4 & \text { if } - 3 \leq x \leq 0 \
\frac { 2 } { 3 } x + 2 & \text { if } 0 < x \leq 3
\end{array} \right.$ 
D) 
$f ( x ) = \left\{ \begin{array} { l l } 
\frac { 4 } { 3 } x + 4 & \text { if } - 3 \leq x \leq 0 \
\frac { 2 } { 3 } x & \text { if } 0 < x \leq 3
\end{array} \right.$

Question 16

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function.
-$$y = 4 f ( x )$$

Accepted Answer

A)  $( 5,3 )$ 
B)  $( 3,8 )$ 
C)  $( 8,4 )$ 
D)  $( 2,16 )$ 
A)  $( 5,3 )$ 
B)  $( 3,8 )$ 
C)  $( 8,4 )$ 
D)  $( 2,16 )$

Question 17

If y varies directly as x, find a linear function which relates them.
-$y = 0.6$ when $x = 1.2$

Accepted Answer

A)  $f ( x ) = 0.6 x$ 
B)  $f ( x ) = 0.5 x$ 
C)  $f ( x ) = x - 0.6$ 
D)  $f ( x ) = 2 x$ 
A)  $f ( x ) = 0.6 x$ 
B)  $f ( x ) = 0.5 x$ 
C)  $f ( x ) = x - 0.6$ 
D)  $f ( x ) = 2 x$

Question 18

The graph of a function f is given. Use the graph to answer the question.
-Is $f ( 3 )$ positive or negative?

Accepted Answer

A)  positive 
B)  negative 
A)  positive 
B)  negative

Question 19

Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$f(x)=7 x^{2}$

Accepted Answer

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

Question 20

Write the word or phrase that best completes each statement or answers the question.
-A cellular phone plan had the following schedule of charges: $\begin{array}{ll}
\text { Basic service, including } 100 \text { minutes of calls } & \$ 20.00 \text { per month } \
2 \text { nd } 100 \text { minutes of calls } & \$ 0.075 \text { per minute } \
\text { Additional minutes of calls } & \$ 0.10 \text { per minute }
\end{array}$ What is the charge for 200 minutes of calls in one month?
What is the charge for 250 minutes of calls in one month?
Construct a function that relates the monthly charge C for x minutes of calls.

Accepted Answer

\[\begin{array} { l } 
\$ 27.50 \
\$ 32

Find an equation of the secant line containing (1, f(1)) and (2, f(2)). - $f ( x ) = \frac { 4 } { x + 3 }$

Answer the question about the given function. -Given the function $f ( x ) = \frac { x ^ { 2 } + 8 } { x - 4 }$ , list the $y$ -intercept, if there is one, of the graph of $f$ .

Determine whether the equation defines y as a function of x. - $\mathrm { y } = \frac { 1 } { \mathrm { x } }$

Choose the one alternative that best completes the statement or answers the question. -A farmer's silo is the shape of a cylinder with a hemisphere as the roof. If the radius of the hemisphere is 10 feet and the height of the silo is heet, express the volume of the silo as a function of h.

The graph of a function f is given. Use the graph to answer the question. -How often does the line y = 20 intersect the graph?

Solve the problem. -If $f ( x ) = 9 x ^ { 3 } + 5 x ^ { 2 } - x + C$ and $f ( - 2 ) = 1$ , what is the value of $C$ ?

Answer the question about the given function. -Given the function $f ( x ) = \frac { x ^ { 2 } + 3 } { x - 8 }$ , what is the domain of $f$ ?

Solve the problem. -Suppose that P(x) represents the percentage of income spent on food in year x and I(x) represents income in year x. Determine a function F that represents total food expenditures in year x.

For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. -

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 7 x + 3 ; g ( x ) = 3 x + 7$ Find $f \cdot g$ .

The graph of a piecewise-defined function is given. Write a definition for the function. -

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. - $y = 4 f ( x )$

If y varies directly as x, find a linear function which relates them. - $y = 0.6$ when $x = 1.2$

The graph of a function f is given. Use the graph to answer the question. -Is $f ( 3 )$ positive or negative?

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 1: Functions and Their Graphs

Find an equation of the secant line containing (1, f(1)) and (2, f(2)). - f(x)=4x+3f ( x ) = \frac { 4 } { x + 3 }f(x)=x+34​

Answer the question about the given function. -Given the function f(x)=x2+8x−4f ( x ) = \frac { x ^ { 2 } + 8 } { x - 4 }f(x)=x−4x2+8​ , list the yyy -intercept, if there is one, of the graph of fff .

Determine whether the equation defines y as a function of x. - y=1x\mathrm { y } = \frac { 1 } { \mathrm { x } }y=x1​

Choose the one alternative that best completes the statement or answers the question. Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=(x+7)2+4f(x)=(x+7)^{2}+4f(x)=(x+7)2+4

Choose the one alternative that best completes the statement or answers the question. -A farmer's silo is the shape of a cylinder with a hemisphere as the roof. If the radius of the hemisphere is 10 feet and the height of the silo is heet, express the volume of the silo as a function of h.

The graph of a function f is given. Use the graph to answer the question. -How often does the line y = 20 intersect the graph?

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=−2(x+1)2−3f(x)=-2(x+1)^{2}-3f(x)=−2(x+1)2−3

Choose the one alternative that best completes the statement or answers the question. Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=(x+2)3f(x)=(x+2)^{3}f(x)=(x+2)3

Solve the problem. -If f(x)=9x3+5x2−x+Cf ( x ) = 9 x ^ { 3 } + 5 x ^ { 2 } - x + Cf(x)=9x3+5x2−x+C and f(−2)=1f ( - 2 ) = 1f(−2)=1 , what is the value of CCC ?

Answer the question about the given function. -Given the function f(x)=x2+3x−8f ( x ) = \frac { x ^ { 2 } + 3 } { x - 8 }f(x)=x−8x2+3​ , what is the domain of fff ?

Solve the problem. -Suppose that P(x) represents the percentage of income spent on food in year x and I(x) represents income in year x. Determine a function F that represents total food expenditures in year x.

For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. -

For the given functions f and g, find the requested function and state its domain. - f(x)=7x+3;g(x)=3x+7f ( x ) = 7 x + 3 ; g ( x ) = 3 x + 7f(x)=7x+3;g(x)=3x+7 Find f⋅gf \cdot gf⋅g .

The graph of a piecewise-defined function is given. Write a definition for the function. -

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. - y=4f(x)y = 4 f ( x )y=4f(x)

If y varies directly as x, find a linear function which relates them. - y=0.6y = 0.6y=0.6 when x=1.2x = 1.2x=1.2

The graph of a function f is given. Use the graph to answer the question. -Is f(3)f ( 3 )f(3) positive or negative?

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=7x2f(x)=7 x^{2}f(x)=7x2

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Find an equation of the secant line containing (1, f(1)) and (2, f(2)). - $f ( x ) = \frac { 4 } { x + 3 }$

Answer the question about the given function. -Given the function $f ( x ) = \frac { x ^ { 2 } + 8 } { x - 4 }$ , list the $y$ -intercept, if there is one, of the graph of $f$ .

Determine whether the equation defines y as a function of x. - $\mathrm { y } = \frac { 1 } { \mathrm { x } }$

Solve the problem. -If $f ( x ) = 9 x ^ { 3 } + 5 x ^ { 2 } - x + C$ and $f ( - 2 ) = 1$ , what is the value of $C$ ?

Answer the question about the given function. -Given the function $f ( x ) = \frac { x ^ { 2 } + 3 } { x - 8 }$ , what is the domain of $f$ ?

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 7 x + 3 ; g ( x ) = 3 x + 7$ Find $f \cdot g$ .

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. - $y = 4 f ( x )$

If y varies directly as x, find a linear function which relates them. - $y = 0.6$ when $x = 1.2$

The graph of a function f is given. Use the graph to answer the question. -Is $f ( 3 )$ positive or negative?