Question 1

Find the inverse of the function.
-$$f ( x ) = 7 x ^ { 2 } + 7 , x \geq 0$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \sqrt { \frac { x - 7 } { 7 } }$ 
B)  Not a one-to-one function 
C)  $f ^ { - 1 } ( x ) = \frac { 7 } { \sqrt { x } - 7 }$ 
D)  $f ^ { - 1 } ( x ) = \sqrt { \frac { 7 } { x - 7 } }$ 
A)  $f ^ { - 1 } ( x ) = \sqrt { \frac { x - 7 } { 7 } }$ 
B)  Not a one-to-one function 
C)  $f ^ { - 1 } ( x ) = \frac { 7 } { \sqrt { x } - 7 }$ 
D)  $f ^ { - 1 } ( x ) = \sqrt { \frac { 7 } { x - 7 } }$

Question 2

Solve the equation
-$\sqrt { 2 x + 15 } - x = 6$

Accepted Answer

A)   x=-7 
B)   x=-7,-3 
C)   x=-3 
D)  No solution 
A)   x=-7 
B)   x=-7,-3 
C)   x=-3 
D)  No solution

Question 3

If f is a one-to-one function and the graph of f lies completely within the second quadrant, then
the graph of f-1 lies completely within the first quadrant.

Accepted Answer

A) True 
 B)False

Question 4

Find the inverse of the function.
-$$f ( x ) = \frac { 4 } { x + 7 }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { x } { 7 + 4 x }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 7 + 4 \mathrm { x } } { \mathrm { x } }$ 
C)  Not a one-to-one function 
D)  $f ^ { - 1 } ( x ) = \frac { - 7 x + 4 } { x }$ 
A)  $f ^ { - 1 } ( x ) = \frac { x } { 7 + 4 x }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 7 + 4 \mathrm { x } } { \mathrm { x } }$ 
C)  Not a one-to-one function 
D)  $f ^ { - 1 } ( x ) = \frac { - 7 x + 4 } { x }$

Question 5

A size 44 dress in Country  C  is size 2 in Country D. A function that converts dress sizes in Country  C  to those in Country D is : $f ( x ) = \frac { x } { 2 } - 20$ . Find a formula for the inverse of this function.

Accepted Answer

A)  $f ^ { - 1 } ( x ) = x + 20$ 
B)  $f ^ { - 1 } ( x ) = 2 x + 20$ 
C)  $f ^ { - 1 } ( x ) = 2 ( x - 20 )$ 
D)  $f ^ { - 1 } ( x ) = 2 ( x + 20 )$ 
A)  $f ^ { - 1 } ( x ) = x + 20$ 
B)  $f ^ { - 1 } ( x ) = 2 x + 20$ 
C)  $f ^ { - 1 } ( x ) = 2 ( x - 20 )$ 
D)  $f ^ { - 1 } ( x ) = 2 ( x + 20 )$

Question 6

$32 ^ { \circ }$ Fahrenheit  = $0 ^ { \circ }$ Celsius. A function that converts temperatures in Celsius to those in Fahrenheit is $f ( x ) = \frac { 9 } { 5 } x + 32$ Fahrenheit. Find a formula for the inverse of this function.

Accepted Answer

A)  $f ^ { - 1 } ( x ) = x + 32$ 
B)  $f ^ { - 1 } ( x ) = \frac { 5 } { 9 } ( x - 32 )$ 
C)  $f ^ { - 1 } ( x ) = \frac { 5 } { 9 } ( x + 32 )$ 
D)  $f ^ { - 1 } ( x ) = \frac { 9 } { 5 } x + 32$ 
A)  $f ^ { - 1 } ( x ) = x + 32$ 
B)  $f ^ { - 1 } ( x ) = \frac { 5 } { 9 } ( x - 32 )$ 
C)  $f ^ { - 1 } ( x ) = \frac { 5 } { 9 } ( x + 32 )$ 
D)  $f ^ { - 1 } ( x ) = \frac { 9 } { 5 } x + 32$

Question 7

Sketch the graph of the pair of functions. Use a dashed line for g(x)
-$f(x)=\sqrt[3]{x}, g(x)=\sqrt[3]{x}+5$

Accepted Answer

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

Question 8

The Fahrenheit temperature,  F , in Siber City in October ranges from  $71 ^ { \circ } \mathrm { F } \text { to } 43 ^ { \circ } \mathrm { F }$.  Write an absolute value inequality whose solution is this range.

Accepted Answer

A)  $| \mathrm { F } - 57 |  43$ 
D)  $| \mathrm { F } - 14 | < 57$ 
A)  $| \mathrm { F } - 57 |  43$ 
D)  $| \mathrm { F } - 14 | < 57$

Question 9

Write the equation of the function g(x) that is transformed from the given function f(x), and whose graph is shown.
-$f(x)=x^{2}$

Accepted Answer

A)  $y = ( x - 5 ) ^ { 2 } - 5$ 
B)  $y = 2 ( x + 5 ) ^ { 2 }$ 
C)  $y = ( x - 2 ) ^ { 2 } - 5$ 
D)  $y = - 2 ( x - 5 ) ^ { 2 }$ 
A)  $y = ( x - 5 ) ^ { 2 } - 5$ 
B)  $y = 2 ( x + 5 ) ^ { 2 }$ 
C)  $y = ( x - 2 ) ^ { 2 } - 5$ 
D)  $y = - 2 ( x - 5 ) ^ { 2 }$

Question 10

Write the equation of the function g(x) that is transformed from the given function f(x), and whose graph is shown.
-$f(x)=x^{2}$

Accepted Answer

A)  $y = ( x + 4 ) ^ { 2 }$ 
B)  $y = ( x - 4 ) ^ { 2 } + 1$ 
C)  $y = x ^ { 2 } - 4$ 
D)  $y = ( x - 4 ) ^ { 2 }$ 
A)  $y = ( x + 4 ) ^ { 2 }$ 
B)  $y = ( x - 4 ) ^ { 2 } + 1$ 
C)  $y = x ^ { 2 } - 4$ 
D)  $y = ( x - 4 ) ^ { 2 }$

Question 11

Explain why the functi $f ( x ) = ( x + 3 ) ^ { 3 } - 1$ is a one-to-one function.

Accepted Answer

Answers will vary. Considering

Question 12

Solve the inequality by using algebraic and graphical methods. Round to three decimal places, if necessary.
-$$| 6 x - 9 | \geq 8$$

Accepted Answer

A)  $x \leq - \frac { 17 } { 6 }$ or $x \geq 8$ 
B)  $x \geq \frac { 17 } { 6 }$ 
C)  $\frac { 1 } { 6 } \leq x \leq \frac { 17 } { 6 }$ 
D)  $x \leq \frac { 1 } { 6 }$ or $x \geq \frac { 17 } { 6 }$ 
A)  $x \leq - \frac { 17 } { 6 }$ or $x \geq 8$ 
B)  $x \geq \frac { 17 } { 6 }$ 
C)  $\frac { 1 } { 6 } \leq x \leq \frac { 17 } { 6 }$ 
D)  $x \leq \frac { 1 } { 6 }$ or $x \geq \frac { 17 } { 6 }$

Question 13

Solve the equation
-$2 x ^ { - 2 } - 3 x ^ { - 1 } - 2 = 0$

Accepted Answer

A)   -$\frac { 1 } { 2 }$, 2 
B)  2 ,$\frac { 1 } { 2 }$ 
C)   -$\frac { 1 } { 2 }$,-2 
D)   -2 ,$\frac { 1 } { 2 }$ 
A)   -$\frac { 1 } { 2 }$, 2 
B)  2 ,$\frac { 1 } { 2 }$ 
C)   -$\frac { 1 } { 2 }$,-2 
D)   -2 ,$\frac { 1 } { 2 }$

Question 14

Provide an appropriate response.
-If f(x) represents the number of digital cable subscribers in a particular town and g(x) represents the number of households in the town, with x equal to the number of years from 2007, then what function represents the
Percent of households in the town with digital cable x years after 2007?

Accepted Answer

A)  $100 f ( x ) g ( x )$ 
B)  $100 \frac { f ( x ) } { g ( x ) }$ 
C)  $100 ( f \circ g ) ( x )$ 
D)  $( f + g ) ( x )$ 
A)  $100 f ( x ) g ( x )$ 
B)  $100 \frac { f ( x ) } { g ( x ) }$ 
C)  $100 ( f \circ g ) ( x )$ 
D)  $( f + g ) ( x )$

Question 15

Write the equation of the function g(x) that is transformed from the given function f(x), and whose graph is shown.
-$f(x)=|x|$

Accepted Answer

A)  $y = | x + 3 |$ 
B)  $y = | x - 3 | + 2$ 
C)  $y = | x | - 3$ 
D)  $y = | x - 3 |$ 
A)  $y = | x + 3 |$ 
B)  $y = | x - 3 | + 2$ 
C)  $y = | x | - 3$ 
D)  $y = | x - 3 |$

Question 16

Encode the message BEWARE OF DOG using the one-to-one function defined by $f ( x ) = x ^ { 3 } - 1$ - Use the alphabet coding method  (A=1, B=2, C=3, ...) . Give the inverse function that the decoder would need when the message is received.

Accepted Answer

7 124 1216

Question 17

Decide whether or not the functions are inverses of each other.
-$f ( x ) = \sqrt { 4 - x } , g ( x ) = 4 - x ^ { 2 }$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 18

Find the specified domain and express it in interval notation.
-If $f ( x ) = - 5 x ^ { 2 } - 7$ and  g(x)=x+5 , evaluate  (f-g)(-3) .

Accepted Answer

A)   -60 
B)  55 
C)   -54 
D)   -44 
A)   -60 
B)  55 
C)   -54 
D)   -44

Question 19

A flare fired from the bottom of a gorge is visible only when the flare is above the rim. If it is fired with an initial velocity of  112 ft/sec  and the gorge is  160 ft deep, during what interval can the flare be seen?
$\left( h ( t ) = - 16 t ^ { 2 } + v 0 t + h 0 . \right)$

Accepted Answer

A)  $6 \sec < \mathrm { t } < 9 \mathrm { sec }$ 
B)  $4 \mathrm { sec } < t < 7 \mathrm { sec }$ 
C)  $2 \mathrm { sec } < t < 5 \mathrm { sec }$ 
D)  $0 \mathrm { sec } < t < 2 \mathrm { sec }$ 
A)  $6 \sec < \mathrm { t } < 9 \mathrm { sec }$ 
B)  $4 \mathrm { sec } < t < 7 \mathrm { sec }$ 
C)  $2 \mathrm { sec } < t < 5 \mathrm { sec }$ 
D)  $0 \mathrm { sec } < t < 2 \mathrm { sec }$

Question 20

The function  f(x)=60x computes the number of minutes in  x hours. The function g(x)=24x  computes the
number of hours in  x days. What is $( f \circ g ) ( \mathrm { x } )$ and what does it compute?

Accepted Answer

A)  $( f \circ g ) ( x )$ =84x ; It computes the number of minutes plus the number of days in x days. 
B)  $( f \circ g ) ( x )$ =1440x ;  It computes the number of minutes in x days. 
C)  $( f \circ g ) ( x )$ =1440x ; It computes the number of days in x minutes. 
D)  $( f \circ g ) ( x )$=1440x2 ; It computes the number of minutes in x days. 
A)  $( f \circ g ) ( x )$ =84x ; It computes the number of minutes plus the number of days in x days. 
B)  $( f \circ g ) ( x )$ =1440x ;  It computes the number of minutes in x days. 
C)  $( f \circ g ) ( x )$ =1440x ; It computes the number of days in x minutes. 
D)  $( f \circ g ) ( x )$=1440x2 ; It computes the number of minutes in x days.

Find the inverse of the function. - $f ( x ) = 7 x ^ { 2 } + 7 , x \geq 0$

Solve the equation - $\sqrt { 2 x + 15 } - x = 6$

If f is a one-to-one function and the graph of f lies completely within the second quadrant, then the graph of f-1 lies completely within the first quadrant.

Find the inverse of the function. - $f ( x ) = \frac { 4 } { x + 7 }$

A size 44 dress in Country C is size 2 in Country D. A function that converts dress sizes in Country C to those in Country D is : $f ( x ) = \frac { x } { 2 } - 20$ . Find a formula for the inverse of this function.

$32 ^ { \circ }$ Fahrenheit = $0 ^ { \circ }$ Celsius. A function that converts temperatures in Celsius to those in Fahrenheit is $f ( x ) = \frac { 9 } { 5 } x + 32$ Fahrenheit. Find a formula for the inverse of this function.

Sketch the graph of the pair of functions. Use a dashed line for g(x) - $f(x)=\sqrt[3]{x}, g(x)=\sqrt[3]{x}+5$ $Sketch the graph of the pair of functions. Use a dashed line for g(x) - f(x)=\sqrt[3]{x}, g(x)=\sqrt[3]{x}+5$

The Fahrenheit temperature, F , in Siber City in October ranges from $71 ^ { \circ } \mathrm { F } \text { to } 43 ^ { \circ } \mathrm { F }$ . Write an absolute value inequality whose solution is this range.

Write the equation of the function g(x) that is transformed from the given function f(x), and whose graph is shown. - $f(x)=x^{2}$ $Write the equation of the function g(x) that is transformed from the given function f(x), and whose graph is shown. - f(x)=x^{2}$

Write the equation of the function g(x) that is transformed from the given function f(x), and whose graph is shown. - $f(x)=x^{2}$ $Write the equation of the function g(x) that is transformed from the given function f(x), and whose graph is shown. - f(x)=x^{2}$

Explain why the functi $f ( x ) = ( x + 3 ) ^ { 3 } - 1$ is a one-to-one function.

Solve the inequality by using algebraic and graphical methods. Round to three decimal places, if necessary. - $| 6 x - 9 | \geq 8$

Solve the equation - $2 x ^ { - 2 } - 3 x ^ { - 1 } - 2 = 0$

Write the equation of the function g(x) that is transformed from the given function f(x), and whose graph is shown. - $f(x)=|x|$

Encode the message BEWARE OF DOG using the one-to-one function defined by $f ( x ) = x ^ { 3 } - 1$ - Use the alphabet coding method (A=1, B=2, C=3, ...) . Give the inverse function that the decoder would need when the message is received.

Decide whether or not the functions are inverses of each other. - $f ( x ) = \sqrt { 4 - x } , g ( x ) = 4 - x ^ { 2 }$

Find the specified domain and express it in interval notation. -If $f ( x ) = - 5 x ^ { 2 } - 7$ and g(x)=x+5 , evaluate (f-g)(-3) .

A flare fired from the bottom of a gorge is visible only when the flare is above the rim. If it is fired with an initial velocity of 112 ft/sec and the gorge is 160 ft deep, during what interval can the flare be seen? $\left( h ( t ) = - 16 t ^ { 2 } + v 0 t + h 0 . \right)$

The function f(x)=60x computes the number of minutes in x hours. The function g(x)=24x computes the number of hours in x days. What is $( f \circ g ) ( \mathrm { x } )$ and what does it compute?

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Exam 4: Additional Topics With Functions

Find the inverse of the function. - f(x)=7x2+7,x≥0f ( x ) = 7 x ^ { 2 } + 7 , x \geq 0f(x)=7x2+7,x≥0

Solve the equation - 2x+15−x=6\sqrt { 2 x + 15 } - x = 62x+15​−x=6

If f is a one-to-one function and the graph of f lies completely within the second quadrant, then the graph of f-1 lies completely within the first quadrant.

Find the inverse of the function. - f(x)=4x+7f ( x ) = \frac { 4 } { x + 7 }f(x)=x+74​

A size 44 dress in Country C is size 2 in Country D. A function that converts dress sizes in Country C to those in Country D is : f(x)=x2−20f ( x ) = \frac { x } { 2 } - 20f(x)=2x​−20 . Find a formula for the inverse of this function.

32∘32 ^ { \circ }32∘ Fahrenheit = 0∘0 ^ { \circ }0∘ Celsius. A function that converts temperatures in Celsius to those in Fahrenheit is f(x)=95x+32f ( x ) = \frac { 9 } { 5 } x + 32f(x)=59​x+32 Fahrenheit. Find a formula for the inverse of this function.

Sketch the graph of the pair of functions. Use a dashed line for g(x) - f(x)=x3,g(x)=x3+5f(x)=\sqrt[3]{x}, g(x)=\sqrt[3]{x}+5f(x)=3x​,g(x)=3x​+5

The Fahrenheit temperature, F , in Siber City in October ranges from 71∘F to 43∘F71 ^ { \circ } \mathrm { F } \text { to } 43 ^ { \circ } \mathrm { F }71∘F to 43∘F . Write an absolute value inequality whose solution is this range.

Write the equation of the function g(x) that is transformed from the given function f(x), and whose graph is shown. - f(x)=x2f(x)=x^{2}f(x)=x2

Write the equation of the function g(x) that is transformed from the given function f(x), and whose graph is shown. - f(x)=x2f(x)=x^{2}f(x)=x2

Explain why the functi f(x)=(x+3)3−1f ( x ) = ( x + 3 ) ^ { 3 } - 1f(x)=(x+3)3−1 is a one-to-one function.

Solve the inequality by using algebraic and graphical methods. Round to three decimal places, if necessary. - ∣6x−9∣≥8| 6 x - 9 | \geq 8∣6x−9∣≥8

Solve the equation - 2x−2−3x−1−2=02 x ^ { - 2 } - 3 x ^ { - 1 } - 2 = 02x−2−3x−1−2=0

Write the equation of the function g(x) that is transformed from the given function f(x), and whose graph is shown. - f(x)=∣x∣f(x)=|x|f(x)=∣x∣

Encode the message BEWARE OF DOG using the one-to-one function defined by f(x)=x3−1f ( x ) = x ^ { 3 } - 1f(x)=x3−1 - Use the alphabet coding method (A=1, B=2, C=3, ...) . Give the inverse function that the decoder would need when the message is received.

Decide whether or not the functions are inverses of each other. - f(x)=4−x,g(x)=4−x2f ( x ) = \sqrt { 4 - x } , g ( x ) = 4 - x ^ { 2 }f(x)=4−x​,g(x)=4−x2

Find the specified domain and express it in interval notation. -If f(x)=−5x2−7f ( x ) = - 5 x ^ { 2 } - 7f(x)=−5x2−7 and g(x)=x+5 , evaluate (f-g)(-3) .

The function f(x)=60x computes the number of minutes in x hours. The function g(x)=24x computes the number of hours in x days. What is (f∘g)(x)( f \circ g ) ( \mathrm { x } )(f∘g)(x) and what does it compute?

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Find the inverse of the function. - $f ( x ) = 7 x ^ { 2 } + 7 , x \geq 0$

Solve the equation - $\sqrt { 2 x + 15 } - x = 6$

Find the inverse of the function. - $f ( x ) = \frac { 4 } { x + 7 }$

A size 44 dress in Country C is size 2 in Country D. A function that converts dress sizes in Country C to those in Country D is : $f ( x ) = \frac { x } { 2 } - 20$ . Find a formula for the inverse of this function.

$32 ^ { \circ }$ Fahrenheit = $0 ^ { \circ }$ Celsius. A function that converts temperatures in Celsius to those in Fahrenheit is $f ( x ) = \frac { 9 } { 5 } x + 32$ Fahrenheit. Find a formula for the inverse of this function.

Sketch the graph of the pair of functions. Use a dashed line for g(x) - $f(x)=\sqrt[3]{x}, g(x)=\sqrt[3]{x}+5$ $Sketch the graph of the pair of functions. Use a dashed line for g(x) - f(x)=\sqrt[3]{x}, g(x)=\sqrt[3]{x}+5$

The Fahrenheit temperature, F , in Siber City in October ranges from $71 ^ { \circ } \mathrm { F } \text { to } 43 ^ { \circ } \mathrm { F }$ . Write an absolute value inequality whose solution is this range.

Write the equation of the function g(x) that is transformed from the given function f(x), and whose graph is shown. - $f(x)=x^{2}$ $Write the equation of the function g(x) that is transformed from the given function f(x), and whose graph is shown. - f(x)=x^{2}$

Write the equation of the function g(x) that is transformed from the given function f(x), and whose graph is shown. - $f(x)=x^{2}$ $Write the equation of the function g(x) that is transformed from the given function f(x), and whose graph is shown. - f(x)=x^{2}$

Explain why the functi $f ( x ) = ( x + 3 ) ^ { 3 } - 1$ is a one-to-one function.

Solve the inequality by using algebraic and graphical methods. Round to three decimal places, if necessary. - $| 6 x - 9 | \geq 8$

Solve the equation - $2 x ^ { - 2 } - 3 x ^ { - 1 } - 2 = 0$

Write the equation of the function g(x) that is transformed from the given function f(x), and whose graph is shown. - $f(x)=|x|$

Encode the message BEWARE OF DOG using the one-to-one function defined by $f ( x ) = x ^ { 3 } - 1$ - Use the alphabet coding method (A=1, B=2, C=3, ...) . Give the inverse function that the decoder would need when the message is received.

Decide whether or not the functions are inverses of each other. - $f ( x ) = \sqrt { 4 - x } , g ( x ) = 4 - x ^ { 2 }$

Find the specified domain and express it in interval notation. -If $f ( x ) = - 5 x ^ { 2 } - 7$ and g(x)=x+5 , evaluate (f-g)(-3) .

The function f(x)=60x computes the number of minutes in x hours. The function g(x)=24x computes the number of hours in x days. What is $( f \circ g ) ( \mathrm { x } )$ and what does it compute?