Question 1

Determine whether the equation defines y as a function of x.
-$$y = \pm \sqrt { 1 - 6 x }$$

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

Find the domain of the function.
-$$f ( x ) = \frac { x } { x ^ { 2 } + 4 }$$

Accepted Answer

A)  {x|x > -4} 
B)  all real numbers 
C)  {x|x ≠-4} 
D)  {x|x ≠ 0} 
A)  {x|x > -4} 
B)  all real numbers 
C)  {x|x ≠-4} 
D)  {x|x ≠ 0}

Question 4

Given the functi is the point (-1, 4) on the graph of f?
-$$f ( x ) = \frac { x ^ { 2 } + 2 } { x - 5 }$$ Given the functi , what is the domain of f?

Accepted Answer

A)  {x|x ≠-5} 
B)  {x|x ≠5} 
C)  {x|x ≠2} 
D)  $$\left\{ x \mid x \neq \frac { 2 } { 5 } \right\}$$ 
A)  {x|x ≠-5} 
B)  {x|x ≠5} 
C)  {x|x ≠2} 
D)  $$\left\{ x \mid x \neq \frac { 2 } { 5 } \right\}$$

Question 5

Find and simplify the difference quotient of f $\frac { f ( x + h ) - f ( x ) } { h }$ , h ≠ 0, for the function.
-f(x) = 4x - 2

Accepted Answer

A)  0 
B)  $4 + \frac { - 4 } { h }$ 
C)  $4 + \frac { 8 ( x - 2 ) } { h }$ 
D)  4 
A)  0 
B)  $4 + \frac { - 4 } { h }$ 
C)  $4 + \frac { 8 ( x - 2 ) } { h }$ 
D)  4

Question 6

Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$f(x)=\frac{1}{5 x}$

Accepted Answer

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

Question 7

Solve.
-If the resistance in an electrical circuit is held constant, the amount of current flowing through the circuit varies directly with the amount of voltage applied to the circuit. When 5 volts are applied to a circuit,
125 milliamperes of current flow through the circuit. Find the new current if the voltage is increased to 12 volts.

Accepted Answer

A)  325 milliamperes 
B)  60 milliamperes 
C)  288 milliamperes 
D)  300 milliamperes 
A)  325 milliamperes 
B)  60 milliamperes 
C)  288 milliamperes 
D)  300 milliamperes

Question 8

For the function, find the average rate of change of f from 1 to x: $\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1$
-f(x) = -8x

Accepted Answer

A)  -8 
B)  0 
C)  $ \frac { - 8 } { x - 1 }$ 
D)  -9 
A)  -8 
B)  0 
C)  $ \frac { - 8 } { x - 1 }$ 
D)  -9

Question 9

Solve the problem.
-A wire of length 8x is bent into the shape of a square. Express the area A of the square as a function of x.

Accepted Answer

A)  $A ( x ) = 2 x ^ { 2 }$ 
B)  $A ( x ) = \frac { 1 } { 16 } x ^ { 2 }$ 
C)  $\mathrm { A } ( \mathrm { x } ) = 4 \mathrm { x } ^ { 2 }$ 
D)  $A ( x ) = 8 x ^ { 2 }$ 
A)  $A ( x ) = 2 x ^ { 2 }$ 
B)  $A ( x ) = \frac { 1 } { 16 } x ^ { 2 }$ 
C)  $\mathrm { A } ( \mathrm { x } ) = 4 \mathrm { x } ^ { 2 }$ 
D)  $A ( x ) = 8 x ^ { 2 }$

Question 10

Solve the problem.
-If f(x) = int(4x), find f(1.2).

Accepted Answer

A)  2 
B)  1 
C)  4 
D)  5 
A)  2 
B)  1 
C)  4 
D)  5

Question 11

The graph of a function f is given. Use the graph to answer the question.
-What is the domain of f?

Accepted Answer

A)  {x|-100 ≤ x ≤ 100} 
B)  all real numbers 
C)  {x|-80 ≤ x ≤110} 
D)  {x|x ≥ 0} 
A)  {x|-100 ≤ x ≤ 100} 
B)  all real numbers 
C)  {x|-80 ≤ x ≤110} 
D)  {x|x ≥ 0}

Question 12

Solve the problem.
-The figure shown here shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 6 units long. Express the area A of the rectangle in terms of x.

Accepted Answer

A)  A(x) = x(3 - x) 
B)  A(x) = 2x(x - 3) 
C) $ A ( x ) = 2 x ^ { 2 }$ 
D)  A(x) = 2x(3 - x) 
A)  A(x) = x(3 - x) 
B)  A(x) = 2x(x - 3) 
C) $ A ( x ) = 2 x ^ { 2 }$ 
D)  A(x) = 2x(3 - x)

Question 13

Solve the problem.
-A farmer's silo is the shape of a cylinder with a hemisphere as the roof. If the height of the silo is 118 feet and the radius of the hemisphere is r feet, express the volume of the silo as a function of r.

Accepted Answer

A)  $V ( r ) = \pi ( 118 - r ) + \frac { 4 } { 3 } \pi r ^ { 2 }$ 
B)  $V ( r ) = 118 \pi r ^ { 2 } + \frac { 8 } { 3 } \pi r ^ { 3 }$ 
C)  $V ( r ) = \pi ( 118 - r ) r ^ { 3 } + \frac { 4 } { 3 } \pi r ^ { 2 }$ 
D)  $V ( r ) = \pi ( 118 - r ) r ^ { 2 } + \frac { 2 } { 3 } \pi r ^ { 3 }$ 
A)  $V ( r ) = \pi ( 118 - r ) + \frac { 4 } { 3 } \pi r ^ { 2 }$ 
B)  $V ( r ) = 118 \pi r ^ { 2 } + \frac { 8 } { 3 } \pi r ^ { 3 }$ 
C)  $V ( r ) = \pi ( 118 - r ) r ^ { 3 } + \frac { 4 } { 3 } \pi r ^ { 2 }$ 
D)  $V ( r ) = \pi ( 118 - r ) r ^ { 2 } + \frac { 2 } { 3 } \pi r ^ { 3 }$

Question 14

If y varies directly as x, find a linear function which relates them.
-y = 5.6 when x = 0.7

Accepted Answer

A)  f(x) = x + 4.9 
B)  f(x) = 8x 
C)  f(x) = 0.7x 
D)  f(x) = 0.125x 
A)  f(x) = x + 4.9 
B)  f(x) = 8x 
C)  f(x) = 0.7x 
D)  f(x) = 0.125x

Question 15

Solve the problem.
-$$\text { If } f ( x ) = 7 x ^ { 3 } + 5 x ^ { 2 } - x + C \text { and } f ( 3 ) = 1$$ hat is the value of C?

Accepted Answer

A)  C = 148 
B)  C = 238 
C)  C = -230 
D)  C = -20 
A)  C = 148 
B)  C = 238 
C)  C = -230 
D)  C = -20

Question 16

The graph of a function is given. Decide whether it is even, odd, or neither.
-

Accepted Answer

A)  even 
B)  odd 
C)  neither 
A)  even 
B)  odd 
C)  neither

Question 17

Solve the problem.
-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 h feet, express the volume of the silo as a function of h.

Accepted Answer

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

Question 18

Find the value for the function.
-$\text { Find } f ( - x ) \text { when } f ( x ) = 3 x ^ { 2 } - 4 x + 5$

Accepted Answer

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

Question 19

Graph the function.
-$f(x)=\left\{\begin{array}{ll}
-x+2 & x<0 \
\sqrt{x}+3 & x \geq 0
\end{array}\right.$

Accepted Answer

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

Question 20

For the given functions f and g, find the requested function and state its domain.
-$f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 8$
Find $\frac { \mathrm { f } } { \mathrm { g } }$.

Accepted Answer

A)  $\left( \frac { f } { g } \right) ( x ) = \frac { 5 x - 8 } { \sqrt { x } } ; \{ x \mid x \geq 0 \}$ 
B)  $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 5 x - 8 } ; \left\{ x \mid x \geq 0 , x \neq \frac { 8 } { 5 } \right\}$ 
C)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 5 \mathrm { x } - 8 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 8 } { 5 } \right\}$ 
D)  $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 5 x - 8 } ; \{ x \mid x \neq 0 \}$ 
A)  $\left( \frac { f } { g } \right) ( x ) = \frac { 5 x - 8 } { \sqrt { x } } ; \{ x \mid x \geq 0 \}$ 
B)  $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 5 x - 8 } ; \left\{ x \mid x \geq 0 , x \neq \frac { 8 } { 5 } \right\}$ 
C)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 5 \mathrm { x } - 8 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 8 } { 5 } \right\}$ 
D)  $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 5 x - 8 } ; \{ x \mid x \neq 0 \}$

Determine whether the equation defines y as a function of x. - $y = \pm \sqrt { 1 - 6 x }$

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

Find the domain of the function. - $f ( x ) = \frac { x } { x ^ { 2 } + 4 }$

Given the functi is the point (-1, 4) on the graph of f? - $f ( x ) = \frac { x ^ { 2 } + 2 } { x - 5 }$ Given the functi , what is the domain of f?

Find and simplify the difference quotient of f $\frac { f ( x + h ) - f ( x ) } { h }$ , h ≠ 0, for the function. -f(x) = 4x - 2

$For the function, find the average rate of change of f from 1 to x: \frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1 -f(x) = -8x$ For the function, find the average rate of change of f from 1 to x: $\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1$ -f(x) = -8x

Solve the problem. -A wire of length 8x is bent into the shape of a square. Express the area A of the square as a function of x.

Solve the problem. -If f(x) = int(4x), find f(1.2).

The graph of a function f is given. Use the graph to answer the question. -What is the domain of f?

Solve the problem. -The figure shown here shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 6 units long. Express the area A of the rectangle in terms of x.

Solve the problem. -A farmer's silo is the shape of a cylinder with a hemisphere as the roof. If the height of the silo is 118 feet and the radius of the hemisphere is r feet, express the volume of the silo as a function of r.

If y varies directly as x, find a linear function which relates them. -y = 5.6 when x = 0.7

Solve the problem. - $\text { If } f ( x ) = 7 x ^ { 3 } + 5 x ^ { 2 } - x + C \text { and } f ( 3 ) = 1$ hat is the value of C?

The graph of a function is given. Decide whether it is even, odd, or neither. -

Solve the problem. -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 h feet, express the volume of the silo as a function of h.

Find the value for the function. - $\text { Find } f ( - x ) \text { when } f ( x ) = 3 x ^ { 2 } - 4 x + 5$

Graph the function. - $f(x)=\left\{\begin{array}{ll}-x+2 & x<0 \\\sqrt{x}+3 & x \geq 0\end{array}\right.$ $Graph the function. - f(x)=\left\{\begin{array}{ll} -x+2 & x<0 \\ \sqrt{x}+3 & x \geq 0 \end{array}\right.$

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 8$ Find $\frac { \mathrm { f } } { \mathrm { g } }$ .

Linear and Quadratic Functions

Polynomial and Rational Functions

Conics

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

Exam 1: Functions and Their Graphs

Determine whether the equation defines y as a function of x. - y=±1−6xy = \pm \sqrt { 1 - 6 x }y=±1−6x​

Determine whether the equation defines y as a function of x. - x=y2x = y ^ { 2 }x=y2

Find the domain of the function. - f(x)=xx2+4f ( x ) = \frac { x } { x ^ { 2 } + 4 }f(x)=x2+4x​

Given the functi is the point (-1, 4) on the graph of f? - f(x)=x2+2x−5f ( x ) = \frac { x ^ { 2 } + 2 } { x - 5 }f(x)=x−5x2+2​ Given the functi , what is the domain of f?

Find and simplify the difference quotient of f f(x+h)−f(x)h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h)−f(x)​ , h ≠ 0, for the function. -f(x) = 4x - 2

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)=15xf(x)=\frac{1}{5 x}f(x)=5x1​

For the function, find the average rate of change of f from 1 to x: f(x)−f(1)x−1,x≠1\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1x−1f(x)−f(1)​,x=1 -f(x) = -8x