Question 1

Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2.
-Shift 18 units up.

Accepted Answer

A)  $f ( x ) = ( x - 18 ) ^ { 2 }$ 
B)  $f ( x ) = x ^ { 2 } + 18$ 
C)  $f ( x ) = x ^ { 2 } - 18$ 
D)  $f ( x ) = ( x + 18 ) ^ { 2 }$ 
A)  $f ( x ) = ( x - 18 ) ^ { 2 }$ 
B)  $f ( x ) = x ^ { 2 } + 18$ 
C)  $f ( x ) = x ^ { 2 } - 18$ 
D)  $f ( x ) = ( x + 18 ) ^ { 2 }$ B

Question 2

Given f(x) and g(x), find the indicated composition and state its domain.
-For $\mathrm { f } ( \mathrm { x } ) = \frac { 1 } { \mathrm { x } - 5 }$ and $g ( x ) = \frac { 7 } { \mathrm { x } }$, what is the domain of $g \cdot \mathrm { f }$ ?

Accepted Answer

A)  $( - \infty , 0 ) \cup \left( 0 , \frac { 7 } { 5 } \right) \cup \left( \frac { 7 } { 5 } , \infty \right)$ 
B)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  $( - \infty , 0 ) \cup ( 0,5 ) \cup ( 5 , \infty )$ 
D)  $( - \infty , 5 ) \cup ( 5 , \infty )$ 
A)  $( - \infty , 0 ) \cup \left( 0 , \frac { 7 } { 5 } \right) \cup \left( \frac { 7 } { 5 } , \infty \right)$ 
B)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  $( - \infty , 0 ) \cup ( 0,5 ) \cup ( 5 , \infty )$ 
D)  $( - \infty , 5 ) \cup ( 5 , \infty )$ D

Question 3

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or
minimum value
-$$f ( x ) = 2 x ^ { 2 } - 4 x + 11$$

Accepted Answer

A)  Maximum, 1 
B)  Minimum, 1 
C)  Maximum, 9 
D)  Minimum, 9 
A)  Maximum, 1 
B)  Minimum, 1 
C)  Maximum, 9 
D)  Minimum, 9 D

Question 4

Without graphing the function, state the shift(s) that are applied to the graph of f(x) = x2 to graph the given function. If
the graph of f(x) = x2 must be rotated about the x-axis, state this.
-$$f ( x ) = x ^ { 2 } - 4$$

Accepted Answer

A)  left 4 units 
B)  up 4 units 
C)  down 4 units 
D)  right 4 units 
A)  left 4 units 
B)  up 4 units 
C)  down 4 units 
D)  right 4 units

Question 5

Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2.
-Shift 7 units to the left.

Accepted Answer

A)  $f ( x ) = ( x + 7 ) ^ { 2 }$ 
B)  $f ( x ) = x ^ { 2 } - 7$ 
C)  $f ( x ) = x ^ { 2 } + 7$ 
D)  $f ( x ) = ( x - 7 ) ^ { 2 }$ 
A)  $f ( x ) = ( x + 7 ) ^ { 2 }$ 
B)  $f ( x ) = x ^ { 2 } - 7$ 
C)  $f ( x ) = x ^ { 2 } + 7$ 
D)  $f ( x ) = ( x - 7 ) ^ { 2 }$

Question 6

For the functions f(x) and g(x), evaluate the indicated function.
-The function P(x) = - 0.3x2 + 39x - 10 describes a companyʹs net monthly profit or loss and the function C(x) = 11x + 10 describes its monthly costs, where x represents the number of units
Produced. The total revenue function, R(x), is such that R(x) = C(x) + P(x). Find R(x).

Accepted Answer

A)  R(x) = 50x + 0.3x2 
B)  R(x) = 50x - 0.3x2 
C)  R(x) = 49x - 0.6x2 
D)  R(x) = 52x - 0.3x2 
A)  R(x) = 50x + 0.3x2 
B)  R(x) = 50x - 0.3x2 
C)  R(x) = 49x - 0.6x2 
D)  R(x) = 52x - 0.3x2

Question 7

Solve the problem.
-John owns a hot dog stand. His profit, in dollars, is given by the function $P ( x ) = - x ^ { 2 } + 14 x + 57$, where $x$ is the number of hot dogs sold. What is the most he can earn?

Accepted Answer

A)  $\$ 99$ 
B)  $\$ 120$ 
C)  $\$ 106$ 
D)  $\$ 49$ 
A)  $\$ 99$ 
B)  $\$ 120$ 
C)  $\$ 106$ 
D)  $\$ 49$

Question 8

Solve the problem.
-A projectile is thrown upward so that its distance (in feet) above the ground after $\mathrm { t }$ seconds is giver by $h ( t ) = - 10 t ^ { 2 } + 260 t$. What is its maximum height?

Accepted Answer

A)  $2500 \mathrm { ft }$ 
B)  $1690 \mathrm { ft }$ 
C)  $58,370 \mathrm { ft }$ 
D)  $5577 \mathrm { ft }$ 
A)  $2500 \mathrm { ft }$ 
B)  $1690 \mathrm { ft }$ 
C)  $58,370 \mathrm { ft }$ 
D)  $5577 \mathrm { ft }$

Question 9

For the functions f(x) and g(x), evaluate the indicated function.
-The amount of money, in billions of dollars, spent on health care that was covered by insurance in a certain country in a particular year can be approximated by the function f(x) = x2 + 14x + 279,
Where x represents the number of years after 2005. The amount of money, in billions of dollars,
Spent on health care that was paid out of pocket in a certain country in a particular year can be
Approximated by the function g(x) = 9x + 149, where again x represents the number of years after
2005. (i) Find $( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } )$. Explain, in your own words, what this function represents.
(ii) Find ( $\mathrm { f } - \mathrm { g } ) ( 60 )$. Explain, in your own words, what this number represents.

Accepted Answer

A)  (i) $( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 23 \mathrm { x } - 428$; this is the difference between health-care costs that are paid out of pocket and those that are covered by insurance, in billions of dollars, $x$ years after $2005 .$
(ii) 1792 ; health-care costs covered by insurance will be $\$ 1,792,000,000,000$ less than health-care costs that are paid out of pocket in $2065 .$ 
B)  (i) $( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = \mathrm { x } ^ { 2 } + 5 \mathrm { x } + 130$; this is the difference between health-care costs covered by insurance and health-care costs that are paid out of pocket, in billions of dollars, $x$ years after $2005 .$
(ii) 4030 ; health-care costs covered by insurance will be $\$ 4,030,000,000,000$ higher than health-care costs that are paid out of pocket in $2065 .$ 
C)  (i) $( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = \mathrm { x } ^ { 2 } + 5 \mathrm { x } + 130$; this is the difference between health-care costs that are paid out of pocket and those that are covered by insurance, in billions of dollars, $x$ years after 2005 .
(ii) 4030 ; health-care costs covered by insurance will be $\$ 4,030,000,000,000$ less than health-care costs that are paid out of pocket in $2065 .$ 
D)  (i) $( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 23 \mathrm { x } - 428$; this is the difference between health-care costs covered by insurance and health-care costs that are paid out of pocket, in billions of dollars, $x$ years after $2005 .$
(ii) 1792 ; health-care costs covered by insurance will be $\$ 1,792,000,000,000$ higher than health-care costs that are paid out of pocket in $2065 .$ 
A)  (i) $( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 23 \mathrm { x } - 428$; this is the difference between health-care costs that are paid out of pocket and those that are covered by insurance, in billions of dollars, $x$ years after $2005 .$
(ii) 1792 ; health-care costs covered by insurance will be $\$ 1,792,000,000,000$ less than health-care costs that are paid out of pocket in $2065 .$ 
B)  (i) $( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = \mathrm { x } ^ { 2 } + 5 \mathrm { x } + 130$; this is the difference between health-care costs covered by insurance and health-care costs that are paid out of pocket, in billions of dollars, $x$ years after $2005 .$
(ii) 4030 ; health-care costs covered by insurance will be $\$ 4,030,000,000,000$ higher than health-care costs that are paid out of pocket in $2065 .$ 
C)  (i) $( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = \mathrm { x } ^ { 2 } + 5 \mathrm { x } + 130$; this is the difference between health-care costs that are paid out of pocket and those that are covered by insurance, in billions of dollars, $x$ years after 2005 .
(ii) 4030 ; health-care costs covered by insurance will be $\$ 4,030,000,000,000$ less than health-care costs that are paid out of pocket in $2065 .$ 
D)  (i) $( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 23 \mathrm { x } - 428$; this is the difference between health-care costs covered by insurance and health-care costs that are paid out of pocket, in billions of dollars, $x$ years after $2005 .$
(ii) 1792 ; health-care costs covered by insurance will be $\$ 1,792,000,000,000$ higher than health-care costs that are paid out of pocket in $2065 .$

Question 10

Given f(x) and g(x), find the indicated composition and state its domain.
-$$f ( x ) = x ^ { 2 } + 1 , g ( x ) = 5 x + 1$$
Find $( f \circ g ) ( x )$.

Accepted Answer

A)  $25 x ^ { 2 } + 10 x + 1$, all real numbers 
B)  $5 x ^ { 2 } + 6$, all real numbers 
C)  $25 x ^ { 2 } + 5 x + 2$, all real numbers 
D)  $25 x ^ { 2 } + 10 x + 2$, all real numbers 
A)  $25 x ^ { 2 } + 10 x + 1$, all real numbers 
B)  $5 x ^ { 2 } + 6$, all real numbers 
C)  $25 x ^ { 2 } + 5 x + 2$, all real numbers 
D)  $25 x ^ { 2 } + 10 x + 2$, all real numbers

Question 11

Given f(x) and g(x), find the indicated composition and state its domain.
-For $f ( x ) = x ^ { 2 } - 25$ and $g ( x ) = 2 x + 3$, what is the domain of $f \circ g$ ?

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $[ 0 , \infty )$ 
C)  $( - 5,5 )$ 
D)  $[ 5 , \infty )$ 
A)  $( - \infty , \infty )$ 
B)  $[ 0 , \infty )$ 
C)  $( - 5,5 )$ 
D)  $[ 5 , \infty )$

Question 12

Solve the problem.
-$$f ( x ) = x ^ { 2 } - 8 ( x \geq 0 )$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } + 8 , \mathrm { x } \geq - 8$ 
B)  $f ^ { - 1 } ( x ) = \sqrt { x + 8 } , x \geq - 8$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } - 8 } , \mathrm { x } \geq 8$ 
D)  $f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } + 8 } , x \geq - 8$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } + 8 , \mathrm { x } \geq - 8$ 
B)  $f ^ { - 1 } ( x ) = \sqrt { x + 8 } , x \geq - 8$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } - 8 } , \mathrm { x } \geq 8$ 
D)  $f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } + 8 } , x \geq - 8$

Question 13

Find the vertex.
-$$f ( x ) = - 5 ( x - 4 ) ^ { 2 } - 6$$

Accepted Answer

A)  $( - 4 , - 6 )$ 
B)  $( 5,4 )$ 
C)  $( 4 , - 6 )$ 
D)  $( - 6,4 )$ 
A)  $( - 4 , - 6 )$ 
B)  $( 5,4 )$ 
C)  $( 4 , - 6 )$ 
D)  $( - 6,4 )$

Question 14

Without graphing the function, state the shift(s) that are applied to the graph of f(x) = x2 to graph the given function. If
the graph of f(x) = x2 must be rotated about the x-axis, state this.
-$$f ( x ) = ( x + 50 ) ^ { 2 } - 90$$

Accepted Answer

A)  left 90 units, up 50 units 
B)  left 50 units, down 90 units 
C)  right 90 units, up 50 units 
D)  right 50 units, down 90 units 
A)  left 90 units, up 50 units 
B)  left 50 units, down 90 units 
C)  right 90 units, up 50 units 
D)  right 50 units, down 90 units

Question 15

Solve the problem.
-$$f ( x ) = ( x - 11 ) ^ { 2 } ( x \geq 11 )$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = x ^ { 2 } + 11 , x \geq - 11$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } + 11 } , \mathrm { x } \geq - 11$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } } + 11 , \mathrm { x } \geq 0$ 
D)  $f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } + 11 } , x \geq - 11$ 
A)  $f ^ { - 1 } ( x ) = x ^ { 2 } + 11 , x \geq - 11$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } + 11 } , \mathrm { x } \geq - 11$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } } + 11 , \mathrm { x } \geq 0$ 
D)  $f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } + 11 } , x \geq - 11$

Question 16

Solve the problem.
-It costs $800 to start up a business of selling hot dogs. Each hot dog costs $0.60 to produce. Find the cost function C(x) = mx + b whose input is the number of hot dogs and whose output is the total
Cost. Use this function to find the cost of producing 300 hot dogs?

Accepted Answer

A)  $18,800 
B)  $180 
C)  $980 
D)  $860 
A)  $18,800 
B)  $180 
C)  $980 
D)  $860

Question 17

Find the x- and y-intercepts. If no x-intercepts exist, state so.
-$$f ( x ) = - x ^ { 2 } - 6 x - 10$$

Accepted Answer

A)  $\left( \frac { 6 \pm \sqrt { 76 } } { 2 } , 0 \right) , ( 0 , - 10 )$ 
B)  $\left( \frac { 6 \pm \sqrt { 76 } } { 2 } , 0 \right) , ( 0,10 )$ 
C)  No x-intercepts, $( 0,10 )$ 
D)  No x-intercepts, $( 0 , - 10 )$ 
A)  $\left( \frac { 6 \pm \sqrt { 76 } } { 2 } , 0 \right) , ( 0 , - 10 )$ 
B)  $\left( \frac { 6 \pm \sqrt { 76 } } { 2 } , 0 \right) , ( 0,10 )$ 
C)  No x-intercepts, $( 0,10 )$ 
D)  No x-intercepts, $( 0 , - 10 )$

Question 18

For the given function f(x), find f-1(x).
-$$f ( x ) = 5 x + 7$$

Accepted Answer

A)  Not a one-to-one function 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } + 7 } { 5 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { x } { 5 } - 7$ 
D)  $f ^ { - 1 } ( x ) = \frac { x - 7 } { 5 }$ 
A)  Not a one-to-one function 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } + 7 } { 5 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { x } { 5 } - 7$ 
D)  $f ^ { - 1 } ( x ) = \frac { x - 7 } { 5 }$

Question 19

Without graphing the function, state the shift(s) that are applied to the graph of f(x) = x2 to graph the given function. If
the graph of f(x) = x2 must be rotated about the x-axis, state this.
-$$f ( x ) = ( x - 6 ) ^ { 2 } - 15$$

Accepted Answer

A)  left 15 units, down 6 units 
B)  right 15 units, down 6 units 
C)  left 6 units, down 15 units 
D)  right 6 units, down 15 units 
A)  left 15 units, down 6 units 
B)  right 15 units, down 6 units 
C)  left 6 units, down 15 units 
D)  right 6 units, down 15 units

Question 20

Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2.
-$$f ( x ) = 2 x + 16 , g ( x ) = \frac { 1 } { 2 } ( x - 16 )$$

Accepted Answer

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

Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2. -Shift 18 units up.

Given f(x) and g(x), find the indicated composition and state its domain. -For $\mathrm { f } ( \mathrm { x } ) = \frac { 1 } { \mathrm { x } - 5 }$ and $g ( x ) = \frac { 7 } { \mathrm { x } }$ , what is the domain of $g \cdot \mathrm { f }$ ?

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value - $f ( x ) = 2 x ^ { 2 } - 4 x + 11$

Without graphing the function, state the shift(s) that are applied to the graph of f(x) = x2 to graph the given function. If the graph of f(x) = x2 must be rotated about the x-axis, state this. - $f ( x ) = x ^ { 2 } - 4$

Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2. -Shift 7 units to the left.

Solve the problem. -John owns a hot dog stand. His profit, in dollars, is given by the function $P ( x ) = - x ^ { 2 } + 14 x + 57$ , where $x$ is the number of hot dogs sold. What is the most he can earn?

Solve the problem. -A projectile is thrown upward so that its distance (in feet) above the ground after $\mathrm { t }$ seconds is giver by $h ( t ) = - 10 t ^ { 2 } + 260 t$ . What is its maximum height?

Given f(x) and g(x), find the indicated composition and state its domain. - $f ( x ) = x ^ { 2 } + 1 , g ( x ) = 5 x + 1$ Find $( f \circ g ) ( x )$ .

Given f(x) and g(x), find the indicated composition and state its domain. -For $f ( x ) = x ^ { 2 } - 25$ and $g ( x ) = 2 x + 3$ , what is the domain of $f \circ g$ ?

Solve the problem. - $f ( x ) = x ^ { 2 } - 8 ( x \geq 0 )$

Find the vertex. - $f ( x ) = - 5 ( x - 4 ) ^ { 2 } - 6$

Without graphing the function, state the shift(s) that are applied to the graph of f(x) = x2 to graph the given function. If the graph of f(x) = x2 must be rotated about the x-axis, state this. - $f ( x ) = ( x + 50 ) ^ { 2 } - 90$

Solve the problem. - $f ( x ) = ( x - 11 ) ^ { 2 } ( x \geq 11 )$

Solve the problem. -It costs $800 to start up a business of selling hot dogs. Each hot dog costs $0.60 to produce. Find the cost function C(x) = mx + b whose input is the number of hot dogs and whose output is the total Cost. Use this function to find the cost of producing 300 hot dogs?

Find the x- and y-intercepts. If no x-intercepts exist, state so. - $f ( x ) = - x ^ { 2 } - 6 x - 10$

For the given function f(x), find f-1(x). - $f ( x ) = 5 x + 7$

Without graphing the function, state the shift(s) that are applied to the graph of f(x) = x2 to graph the given function. If the graph of f(x) = x2 must be rotated about the x-axis, state this. - $f ( x ) = ( x - 6 ) ^ { 2 } - 15$

Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2. - $f ( x ) = 2 x + 16 , g ( x ) = \frac { 1 } { 2 } ( x - 16 )$

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Exponents and Polynomials

Factoring and Quadratic Equations

Rational Expressions and Equations

A Transition

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 11: Functions

Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2. -Shift 18 units up.

Given f(x) and g(x), find the indicated composition and state its domain. -For f(x)=1x−5\mathrm { f } ( \mathrm { x } ) = \frac { 1 } { \mathrm { x } - 5 }f(x)=x−51​ and g(x)=7xg ( x ) = \frac { 7 } { \mathrm { x } }g(x)=x7​ , what is the domain of g⋅fg \cdot \mathrm { f }g⋅f ?

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value - f(x)=2x2−4x+11f ( x ) = 2 x ^ { 2 } - 4 x + 11f(x)=2x2−4x+11

Without graphing the function, state the shift(s) that are applied to the graph of f(x) = x2 to graph the given function. If the graph of f(x) = x2 must be rotated about the x-axis, state this. - f(x)=x2−4f ( x ) = x ^ { 2 } - 4f(x)=x2−4