Question 1

For the given functions f and g, find the requested function and state its domain.
-$$f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 2$$
Find $\frac { f } { g }$.

Accepted Answer

A)  $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 5 x - 2 } ; \{ x \mid x \neq 0 \}$ 
B)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 5 \mathrm { x } - 2 } ; \left\{ \mathrm { x } \mid \mathrm { x } \geq 0 , \mathrm { x } \neq \frac { 2 } { 5 } \right\}$ 
C)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 5 \mathrm { x } - 2 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 2 } { 5 } \right\}$ 
D)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 5 \mathrm { x } - 2 } { \sqrt { \mathrm { x } } } ; \{ \mathrm { x } \mid \mathrm { x } \geq 0 \}$ 
A)  $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 5 x - 2 } ; \{ x \mid x \neq 0 \}$ 
B)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 5 \mathrm { x } - 2 } ; \left\{ \mathrm { x } \mid \mathrm { x } \geq 0 , \mathrm { x } \neq \frac { 2 } { 5 } \right\}$ 
C)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 5 \mathrm { x } - 2 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 2 } { 5 } \right\}$ 
D)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 5 \mathrm { x } - 2 } { \sqrt { \mathrm { x } } } ; \{ \mathrm { x } \mid \mathrm { x } \geq 0 \}$

Question 2

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 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.
-$f(x)=|x+6|-6$

A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 4

Find the value for the function.
-Find $f ( x + h )$ when $f ( x ) = 2 x ^ { 2 } + 3 x - 3$

Accepted Answer

A)  $2 x ^ { 2 } + 2 h ^ { 2 } + 7 x + 7 h - 3$ 
B)  $2 x ^ { 2 } + 2 h ^ { 2 } + 3 x + 3 h - 3$ 
C)  $2 x ^ { 2 } + 4 x h + 2 h ^ { 2 } + 3 x + 3 h - 3$ 
D)  $2 x ^ { 2 } + 2 x h + 2 h ^ { 2 } + 3 x + 3 h - 3$ 
A)  $2 x ^ { 2 } + 2 h ^ { 2 } + 7 x + 7 h - 3$ 
B)  $2 x ^ { 2 } + 2 h ^ { 2 } + 3 x + 3 h - 3$ 
C)  $2 x ^ { 2 } + 4 x h + 2 h ^ { 2 } + 3 x + 3 h - 3$ 
D)  $2 x ^ { 2 } + 2 x h + 2 h ^ { 2 } + 3 x + 3 h - 3$

Question 5

Determine whether the equation defines y as a function of x.
-$y=7 x^{2}-2 x+8$

Accepted Answer

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

Question 6

Solve the problem.
-If $f ( x ) = \frac { x - 4 A } { - 12 x + 3 }$ and $f ( - 12 ) = - 4$, what is the value of $A$ ?

Accepted Answer

A)  $\mathrm { A } = - 144$ 
B)  $A = - 150$ 
C)  $\mathrm { A } = 150$ 
D)  $\mathrm { A } = 144$ 
A)  $\mathrm { A } = - 144$ 
B)  $A = - 150$ 
C)  $\mathrm { A } = 150$ 
D)  $\mathrm { A } = 144$

Question 7

Find the value for the function.
-$\text { Find } f(-x) \text { when } f(x)=\frac{x}{x^{2}+1}$

Accepted Answer

A)  $\frac{-x}{x^{2}+1}$ 
B) $\frac{-x}{x^{2}-1}$ 
C)  $\frac{-x}{-x^{2}+1}$ 
D)  $\frac{x}{-x^{2}+1}$ 
A)  $\frac{-x}{x^{2}+1}$ 
B) $\frac{-x}{x^{2}-1}$ 
C)  $\frac{-x}{-x^{2}+1}$ 
D)  $\frac{x}{-x^{2}+1}$

Question 8

Find the domain of the function.
-$$h ( x ) = \frac { x - 2 } { x ^ { 3 } - 9 x }$$

Accepted Answer

A)  $\{ x \mid x \neq 2 \}$ 
B)  $\{ x \mid x \neq 0 \}$ 
C)  all real numbers 
D)  $\{ x \mid x \neq - 3,0,3 \}$ 
A)  $\{ x \mid x \neq 2 \}$ 
B)  $\{ x \mid x \neq 0 \}$ 
C)  all real numbers 
D)  $\{ x \mid x \neq - 3,0,3 \}$

Question 9

Solve the problem.
-A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 11 inches by 24 inches by cutting out equal squares of side x at each corner and then folding up the sides as in the figure.
Express the volume V of the box as a function of x.   A) $V ( x ) = x ( 11 - 2 x ) ( 24 - 2 x )$

Accepted Answer

B)  $V ( x ) = ( 11 - x ) ( 24 - x )$ 
C)  $V ( x ) = ( 11 - 2 x ) ( 24 - 2 x )$ 
D)  $V ( x ) = x ( 11 - x ) ( 24 - x )$ 
B)  $V ( x ) = ( 11 - x ) ( 24 - x )$ 
C)  $V ( x ) = ( 11 - 2 x ) ( 24 - 2 x )$ 
D)  $V ( x ) = x ( 11 - x ) ( 24 - x )$

Question 10

Graph the function.
-$f(x)=\left\{\begin{array}{ll}
x+1 & \text { if }-8 \leq x6
\end{array}\right.$

A)

Accepted Answer

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

Question 11

For the given functions f and g, find the requested function and state its domain.
-$$f ( x ) = \sqrt { x + 7 } ; g ( x ) = \frac { 2 } { x }$$
Find $\mathrm { f } \cdot \mathrm { g }$.

Accepted Answer

A)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = \frac { \sqrt { 2 \mathrm { x } + 14 } } { \mathrm { x } } ; \{ \mathrm { x } \mid \mathrm { x } \geq - 7 , \mathrm { x } \neq 0 \}$ 
B)  $( f \cdot g ) ( x ) = \frac { 2 \sqrt { x + 7 } } { x } ; \{ x \mid x \geq - 7 , x \neq 0 \}$ 
C)  $( f \cdot g ) ( x ) = \sqrt { \frac { 9 } { x } } ; \{ x \mid x \neq 0 \}$ 
D)  $( f \cdot g ) ( x ) = \sqrt { \frac { 2 x + 14 } { x } } ; \{ x \mid x \geq - 7 , x \neq 0 \}$ 
A)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = \frac { \sqrt { 2 \mathrm { x } + 14 } } { \mathrm { x } } ; \{ \mathrm { x } \mid \mathrm { x } \geq - 7 , \mathrm { x } \neq 0 \}$ 
B)  $( f \cdot g ) ( x ) = \frac { 2 \sqrt { x + 7 } } { x } ; \{ x \mid x \geq - 7 , x \neq 0 \}$ 
C)  $( f \cdot g ) ( x ) = \sqrt { \frac { 9 } { x } } ; \{ x \mid x \neq 0 \}$ 
D)  $( f \cdot g ) ( x ) = \sqrt { \frac { 2 x + 14 } { x } } ; \{ x \mid x \geq - 7 , x \neq 0 \}$

Question 12

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.
-$f(x)=|x-2|$

A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 13

Find the domain of the function.
-$$f ( x ) = \left\{ \begin{array} { l l } 
2 x & \text { if } x \neq 0 \
2 & \text { if } x = 0
\end{array} \right.$$

Accepted Answer

A)  $\{ x \mid x \neq 0 \}$ 
B)  all real numbers 
C)  $\{ x \mid x \leq 0 \}$ 
D)  $\{ 0 \}$ 
A)  $\{ x \mid x \neq 0 \}$ 
B)  all real numbers 
C)  $\{ x \mid x \leq 0 \}$ 
D)  $\{ 0 \}$

Question 14

If y varies directly as x, find a linear function which relates them.
-$$y = 2 \text { when } x = \frac { 1 } { 9 }$$

Accepted Answer

A)  $f ( x ) = \frac { x } { 18 }$ 
B)  $f ( x ) = \frac { x } { 2 }$ 
C)  $f ( x ) = 18 x$ 
D)  $f ( x ) = x + \frac { 17 } { 9 }$ 
A)  $f ( x ) = \frac { x } { 18 }$ 
B)  $f ( x ) = \frac { x } { 2 }$ 
C)  $f ( x ) = 18 x$ 
D)  $f ( x ) = x + \frac { 17 } { 9 }$

Question 15

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. A) $F ( x ) = ( P + I ) ( x )$

Accepted Answer

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

Question 16

Solve the problem.
-A rocket is shot straight up in the air from the ground at a rate of 80 feet per second. The rocket is tracked by a range finder that is 431 feet from the launch pad. Let d represent the distance from the rocket to the range finder
And t represent the time, in seconds, since "blastoff". Express d as a function of t. A) $\mathrm { d } ( \mathrm { t } ) = 431 ^ { 2 } + ( 80 \mathrm { t } ) ^ { 2 }$

Accepted Answer

B)  $d ( t ) = \sqrt { 80 ^ { 2 } + ( 431 t ) ^ { 2 } }$ 
C)  $\mathrm { d } ( \mathrm { t } ) = 431 + 80 \mathrm { t } ^ { 2 }$ 
D)  $\mathrm { d } ( \mathrm { t } ) = \sqrt { 431 ^ { 2 } + ( 80 \mathrm { t } ) ^ { 2 } }$ 
B)  $d ( t ) = \sqrt { 80 ^ { 2 } + ( 431 t ) ^ { 2 } }$ 
C)  $\mathrm { d } ( \mathrm { t } ) = 431 + 80 \mathrm { t } ^ { 2 }$ 
D)  $\mathrm { d } ( \mathrm { t } ) = \sqrt { 431 ^ { 2 } + ( 80 \mathrm { t } ) ^ { 2 } }$

Question 17

Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.
-  A)
$\begin{array}{l}
\text { function } \
\text { domain: all real numbers } \
\text { range: }\{\mathrm{y} \mid \mathrm{y} \leq 9\} \
\text { intercepts: }(0,-4),(8,0),(0,2) \
\text { symmetry: none }
\end{array}$

Accepted Answer

B) 
function
domain: $ \{x \mid x \leq 9\} $
range: all real numbers
intercepts: $ (-4,0),(0,8),(2,0) $
symmetry: $ y $-axis 
C) 
function
domain: all real numbers
range: $ \{y \mid y \leq 9\} $
intercepts: $ (-4,0),(0,8),(2,0) $
symmetry: none 
D)  not function 
B) 
function
domain: $ \{x \mid x \leq 9\} $
range: all real numbers
intercepts: $ (-4,0),(0,8),(2,0) $
symmetry: $ y $-axis 
C) 
function
domain: all real numbers
range: $ \{y \mid y \leq 9\} $
intercepts: $ (-4,0),(0,8),(2,0) $
symmetry: none 
D)  not function

Question 18

Determine whether the equation defines y as a function of x.
-$y=\pm \sqrt{1-5 x}$

Accepted Answer

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

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.
-$f(x)=6 x^{3}$
 
 A)

Accepted Answer

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

Question 20

Answer the question about the given function.
-Given the functi $$f ( x ) = - 5 x ^ { 2 } + 10 x - 1$$ , if x = 1, what is f(x)? What point is on the graph of f?

Accepted Answer

A)  4; (1, 4) 
B)  4; (4, 1) 
C)  -16; (-16, 1) 
D)  -16; (1, -16) 
A)  4; (1, 4) 
B)  4; (4, 1) 
C)  -16; (-16, 1) 
D)  -16; (1, -16)

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 2$ Find $\frac { f } { g }$ .

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

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. - $f(x)=|x+6|-6$ A) B) C) D)

Find the value for the function. -Find $f ( x + h )$ when $f ( x ) = 2 x ^ { 2 } + 3 x - 3$

Determine whether the equation defines y as a function of x. - $y=7 x^{2}-2 x+8$

Solve the problem. -If $f ( x ) = \frac { x - 4 A } { - 12 x + 3 }$ and $f ( - 12 ) = - 4$ , what is the value of $A$ ?

Find the value for the function. - $\text { Find } f(-x) \text { when } f(x)=\frac{x}{x^{2}+1}$

Find the domain of the function. - $h ( x ) = \frac { x - 2 } { x ^ { 3 } - 9 x }$

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \sqrt { x + 7 } ; g ( x ) = \frac { 2 } { x }$ Find $\mathrm { f } \cdot \mathrm { g }$ .

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. - $f(x)=|x-2|$ A) B) C) D)

Find the domain of the function. - $f ( x ) = \left\{ \begin{array} { l l } 2 x & \text { if } x \neq 0 \\2 & \text { if } x = 0\end{array} \right.$

If y varies directly as x, find a linear function which relates them. - $y = 2 \text { when } x = \frac { 1 } { 9 }$

Determine whether the equation defines y as a function of x. - $y=\pm \sqrt{1-5 x}$

Answer the question about the given function. -Given the functi $f ( x ) = - 5 x ^ { 2 } + 10 x - 1$ , if x = 1, what is f(x)? What point is on the graph of f?

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

Review

Filters

Exam 1: Functions and Their Graphs

For the given functions f and g, find the requested function and state its domain. - f(x)=x;g(x)=5x−2f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 2f(x)=x​;g(x)=5x−2 Find fg\frac { f } { g }gf​ .

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)

Find the value for the function. -Find f(x+h)f ( x + h )f(x+h) when f(x)=2x2+3x−3f ( x ) = 2 x ^ { 2 } + 3 x - 3f(x)=2x2+3x−3

Determine whether the equation defines y as a function of x. - y=7x2−2x+8y=7 x^{2}-2 x+8y=7x2−2x+8

Solve the problem. -If f(x)=x−4A−12x+3f ( x ) = \frac { x - 4 A } { - 12 x + 3 }f(x)=−12x+3x−4A​ and f(−12)=−4f ( - 12 ) = - 4f(−12)=−4 , what is the value of AAA ?

Find the value for the function. - Find f(−x) when f(x)=xx2+1\text { Find } f(-x) \text { when } f(x)=\frac{x}{x^{2}+1} Find f(−x) when f(x)=x2+1x​

Find the domain of the function. - h(x)=x−2x3−9xh ( x ) = \frac { x - 2 } { x ^ { 3 } - 9 x }h(x)=x3−9xx−2​

Graph the function. - f(x)={x+1 if −8≤x<6−5 if x=6−x+10 if x>6f(x)=\left\{\begin{array}{ll}x+1 & \text { if }-8 \leq x<6 \\-5 & \text { if } x=6 \\-x+10 & \text { if } x>6\end{array}\right.f(x)=⎩⎨⎧​x+1−5−x+10​ if −8≤x<6 if x=6 if x>6​ A) B) C) D)

For the given functions f and g, find the requested function and state its domain. - f(x)=x+7;g(x)=2xf ( x ) = \sqrt { x + 7 } ; g ( x ) = \frac { 2 } { x }f(x)=x+7​;g(x)=x2​ Find f⋅g\mathrm { f } \cdot \mathrm { g }f⋅g .

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∣f(x)=|x-2|f(x)=∣x−2∣ A) B) C) D)

Find the domain of the function. - f(x)={2x if x≠02 if x=0f ( x ) = \left\{ \begin{array} { l l } 2 x & \text { if } x \neq 0 \\2 & \text { if } x = 0\end{array} \right.f(x)={2x2​ if x=0 if x=0​

If y varies directly as x, find a linear function which relates them. - y=2 when x=19y = 2 \text { when } x = \frac { 1 } { 9 }y=2 when x=91​

Determine whether the equation defines y as a function of x. - y=±1−5xy=\pm \sqrt{1-5 x}y=±1−5x​

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)=6x3f(x)=6 x^{3}f(x)=6x3 A) B) C) D)

Answer the question about the given function. -Given the functi f(x)=−5x2+10x−1f ( x ) = - 5 x ^ { 2 } + 10 x - 1f(x)=−5x2+10x−1 , if x = 1, what is f(x)? What point is on the graph of f?