Question 1

Find the x- and y-intercepts. If no x-intercepts exist, state so.
-$$f ( x ) = 2 x ^ { 2 } - 4 x - 48$$

Accepted Answer

A)  $( 6,0 ) , ( - 4,0 ) , ( 0 , - 48 )$ 
B)  $( - 6,0 ) , ( - 4,0 ) , ( 0,48 )$ 
C)  $( 6,0 ) , ( 4,0 ) , ( 0,48 )$ 
D)  $( - 6,0 ) , ( 4,0 ) , ( 0 , - 48 )$ 
A)  $( 6,0 ) , ( - 4,0 ) , ( 0 , - 48 )$ 
B)  $( - 6,0 ) , ( - 4,0 ) , ( 0,48 )$ 
C)  $( 6,0 ) , ( 4,0 ) , ( 0,48 )$ 
D)  $( - 6,0 ) , ( 4,0 ) , ( 0 , - 48 )$

Question 2

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

Accepted Answer

A)  $( - 5 , - 2 )$ 
B)  $( - 2,5 )$ 
C)  $( 5 , - 4 )$ 
D)  $( - 5,2 )$ 
A)  $( - 5 , - 2 )$ 
B)  $( - 2,5 )$ 
C)  $( 5 , - 4 )$ 
D)  $( - 5,2 )$

Question 3

Solve the problem.
-$$f ( x ) = ( x + 11 ) ^ { 2 } - 3 ( x \geq - 11 )$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } + 3 } - 11 , \mathrm { x } \geq - 3$ 
B)  $f ^ { - 1 } ( x ) = \sqrt { x - 3 } + 11 , x \geq 3$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 3 \mathrm { x } ^ { 2 } + 11 , \mathrm { x } \geq 0$ 
D)  $f ^ { - 1 } ( x ) = \sqrt { x + 11 } + 3 , x \geq - 11$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } + 3 } - 11 , \mathrm { x } \geq - 3$ 
B)  $f ^ { - 1 } ( x ) = \sqrt { x - 3 } + 11 , x \geq 3$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 3 \mathrm { x } ^ { 2 } + 11 , \mathrm { x } \geq 0$ 
D)  $f ^ { - 1 } ( x ) = \sqrt { x + 11 } + 3 , x \geq - 11$

Question 4

For the given functions f(x) and g(x), find (f ∙ g)(x) or $ \left(\frac{f}{g}\right)(x) $ as indicated.
-$$f ( x ) = ( x + 3 ) ^ { 2 }$$

Accepted Answer

A)  Domain: $( - \infty , \infty )$
Range: $( - \infty , \infty )$ 
B)  Domain: $( - \infty , \infty )$ 
 Range: $[ 0 , \infty )$ 
C)  Domain: $[ - 3 , \infty )$
Range: $( - \infty , \infty )$ 
D)  Domain: $( - \infty , \infty )$
Range: $[ 3 , \infty )$ 
A)  Domain: $( - \infty , \infty )$
Range: $( - \infty , \infty )$ 
B)  Domain: $( - \infty , \infty )$ 
 Range: $[ 0 , \infty )$ 
C)  Domain: $[ - 3 , \infty )$
Range: $( - \infty , \infty )$ 
D)  Domain: $( - \infty , \infty )$
Range: $[ 3 , \infty )$

Question 5

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.
-$$f ( x ) = ( x - 6 ) ^ { 2 } + 11$$

Accepted Answer

A)  right 11 units, down 6 units 
B)  left 6 units, up 11 units 
C)  right 6 units, up 11 units 
D)  rotate about x-axis, right 6 units, up 11 units 
A)  right 11 units, down 6 units 
B)  left 6 units, up 11 units 
C)  right 6 units, up 11 units 
D)  rotate about x-axis, right 6 units, up 11 units

Question 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.
-$$f ( x ) = - ( x - 2 ) ^ { 2 } + 5$$

Accepted Answer

A)  right 2 units, up 5 units 
B)  rotate about x-axis, left 2 units, up 5 units 
C)  right 5 units, down 2 units 
D)  rotate about x-axis, right 2 units, up 5 units 
A)  right 2 units, up 5 units 
B)  rotate about x-axis, left 2 units, up 5 units 
C)  right 5 units, down 2 units 
D)  rotate about x-axis, right 2 units, up 5 units

Question 7

Given f(x) and g(x), find the indicated composition and state its domain.
-For $f ( x ) = 5 \sqrt { x + 3 }$ and $g ( x ) = 2 x + 9$, what is the domain of $g \circ f$ ?

Accepted Answer

A)  $[ - 12 , \infty )$ 
B)  $( - 3 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $[ - 3 , \infty )$ 
A)  $[ - 12 , \infty )$ 
B)  $( - 3 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $[ - 3 , \infty )$

Question 8

Solve the problem.
-A projectile is thrown upward so that its distance above the ground after t sec is given by $$h ( t ) = - 13 t ^ { 2 } + 364 t$$

Accepted Answer

A)  21 sec 
B)  14 sec 
C)  28 sec 
D)  7 sec 
A)  21 sec 
B)  14 sec 
C)  28 sec 
D)  7 sec

Question 9

Find the x- and y-intercepts. If no x-intercepts exist, state so.
-$$f ( x ) = 6 x ^ { 2 } + 12 x + 3$$

Accepted Answer

A)  $\left( \frac { - 12 \pm \sqrt { 2 } } { 2 } , 0 \right) , ( 0,3 )$ 
B)  $\left( \frac { - 2 \pm \sqrt { 2 } } { 2 } , 0 \right) , ( 0,3 )$ 
C)  $\left( \frac { - 2 \pm \sqrt { 2 } } { 12 } , 0 \right) , ( 0 , - 3 )$ 
D)  $\left( \frac { - 2 \pm \sqrt { 6 } } { 2 } , 0 \right\} , ( 0 , - 3 )$ 
A)  $\left( \frac { - 12 \pm \sqrt { 2 } } { 2 } , 0 \right) , ( 0,3 )$ 
B)  $\left( \frac { - 2 \pm \sqrt { 2 } } { 2 } , 0 \right) , ( 0,3 )$ 
C)  $\left( \frac { - 2 \pm \sqrt { 2 } } { 12 } , 0 \right) , ( 0 , - 3 )$ 
D)  $\left( \frac { - 2 \pm \sqrt { 6 } } { 2 } , 0 \right\} , ( 0 , - 3 )$

Question 10

Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2.
-Shift 66 units to the left and 72 units down.

Accepted Answer

A)  $f ( x ) = ( x - 66 ) ^ { 2 } - 72$ 
B)  $f ( x ) = ( x - 72 ) ^ { 2 } - 66$ 
C)  $f ( x ) = ( x + 66 ) ^ { 2 } - 72$ 
D)  $f ( x ) = ( x - 72 ) ^ { 2 } + 66$ 
A)  $f ( x ) = ( x - 66 ) ^ { 2 } - 72$ 
B)  $f ( x ) = ( x - 72 ) ^ { 2 } - 66$ 
C)  $f ( x ) = ( x + 66 ) ^ { 2 } - 72$ 
D)  $f ( x ) = ( x - 72 ) ^ { 2 } + 66$

Question 11

For the given function f(x), find f-1(x).
-$$f ( x ) = \frac { 3 x + 6 } { 6 x + 9 }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { - 9 x + 6 } { 6 x - 3 }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 3 \mathrm { x } + 6 } { 6 \mathrm { x } + 9 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 6 x - 3 } { - 9 x + 6 }$ 
D)  Not one-to-one 
A)  $f ^ { - 1 } ( x ) = \frac { - 9 x + 6 } { 6 x - 3 }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 3 \mathrm { x } + 6 } { 6 \mathrm { x } + 9 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 6 x - 3 } { - 9 x + 6 }$ 
D)  Not one-to-one

Question 12

Solve the problem.
-A driver wants to gauge the fuel efficiency of her vehicle at speeds of 30 mph and above. She notices that traveling at an average speed of 30 mph results in a rating of 29 mpg, where as at an Average speed of 35 mph, her car rates 19 mpg. Find a linear function f(x)= mx + b whose input is
The speed in miles per hour and whose output is the gas mileage in miles per gallon.

Accepted Answer

A)  $f ( x ) = \frac { 1 } { 2 } x + 89$ 
B)  $f ( x ) = - 2 x + 31$ 
C)  $f ( x ) = - 2 x + 89$ 
D)  $f ( x ) = \frac { 1 } { 2 } x + 31$ 
A)  $f ( x ) = \frac { 1 } { 2 } x + 89$ 
B)  $f ( x ) = - 2 x + 31$ 
C)  $f ( x ) = - 2 x + 89$ 
D)  $f ( x ) = \frac { 1 } { 2 } x + 31$

Question 13

Given f(x) and g(x), find the indicated composition and state its domain.
-For $f ( x ) = 5 x - 5$ and $g ( x ) = 2 x + 5$, what is the domain of $f \cdot g$ ?

Accepted Answer

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

Question 14

For the given functions f(x) and g(x), find (f ∙ g)(x) or $ \left(\frac{f}{g}\right)(x) $ as indicated.
-$$f ( x ) = - 7 x + 4 , g ( x ) = 5 x ^ { 2 } - x + 5$$
Find $( f \cdot g ) ( x )$.

Accepted Answer

A)  $- 35 x ^ { 3 } + 27 x ^ { 2 } - 39 x + 20$ 
B)  $- 35 x ^ { 3 } + 13 x ^ { 2 } - 39 x + 20$ 
C)  $- 35 x ^ { 3 } - 39 x + 20$ 
D)  $12 x ^ { 2 } - 39 x + 20$ 
A)  $- 35 x ^ { 3 } + 27 x ^ { 2 } - 39 x + 20$ 
B)  $- 35 x ^ { 3 } + 13 x ^ { 2 } - 39 x + 20$ 
C)  $- 35 x ^ { 3 } - 39 x + 20$ 
D)  $12 x ^ { 2 } - 39 x + 20$

Question 15

Solve the problem.
-An electrician charges a fee of $45 plus $30 per hour. Find a linear function f(x) = mx + b whose input is the number of hours worked and whose output is the total cost of the job. Find the Slope-intercept form of the equation.

Accepted Answer

A)  $f ( x ) = 45 x - 30$ 
B)  $f ( x ) = 45 x + 30$ 
C)  $f ( x ) = 30 x - 45$ 
D)  $f ( x ) = 30 x + 45$ 
A)  $f ( x ) = 45 x - 30$ 
B)  $f ( x ) = 45 x + 30$ 
C)  $f ( x ) = 30 x - 45$ 
D)  $f ( x ) = 30 x + 45$

Question 16

Given f(x) and g(x), find the indicated composition and state its domain.
-$$f ( x ) = 7 x + 10 , g ( x ) = 3 x - 1$$
Find $( f \circ g ) ( x )$.

Accepted Answer

A)  $21 x + 29$, all real numbers 
B)  $21 x + 9$, all real numbers 
C)  $21 x + 17$, all real numbers 
D)  $21 x + 3$, all real numbers 
A)  $21 x + 29$, all real numbers 
B)  $21 x + 9$, all real numbers 
C)  $21 x + 17$, all real numbers 
D)  $21 x + 3$, all real numbers

Question 17

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

Accepted Answer

A)  $( 0 , \pm \sqrt { 2 } ) , ( 0 , - 2 )$ 
B)  $( \pm \sqrt { 2 } , 0 ) , ( 0,2 )$ 
C)  $( 0 , \pm \sqrt { 2 } ) , ( 0,2 )$ 
D)  $( \pm \sqrt { 2 } , 0 ) , ( 0 , - 2 )$ 
A)  $( 0 , \pm \sqrt { 2 } ) , ( 0 , - 2 )$ 
B)  $( \pm \sqrt { 2 } , 0 ) , ( 0,2 )$ 
C)  $( 0 , \pm \sqrt { 2 } ) , ( 0,2 )$ 
D)  $( \pm \sqrt { 2 } , 0 ) , ( 0 , - 2 )$

Question 18

Given f(x) and g(x), find the indicated composition and state its domain.
-For $f ( x ) = \frac { 1 } { x - 7 }$ and $g ( x ) = \frac { 9 } { x }$, what is the domain of $f \circ g$ ?

Accepted Answer

A)  $\left( 0 , \frac { 9 } { 7 } \right) \cup \left( \frac { 9 } { 7 } , \infty \right)$ 
B)  $( - \infty , 0 ) \cup ( 0,7 ) \cup ( 7 , \infty )$ 
C)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  $( - \infty , 0 ) \cup \left( 0 , \frac { 9 } { 7 } \right) \cup \left( \frac { 9 } { 7 } , \infty \right)$ 
A)  $\left( 0 , \frac { 9 } { 7 } \right) \cup \left( \frac { 9 } { 7 } , \infty \right)$ 
B)  $( - \infty , 0 ) \cup ( 0,7 ) \cup ( 7 , \infty )$ 
C)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  $( - \infty , 0 ) \cup \left( 0 , \frac { 9 } { 7 } \right) \cup \left( \frac { 9 } { 7 } , \infty \right)$

Question 19

For the functions f(x) and g(x), evaluate the indicated function.
-Find $\left( \frac { f } { g } \right) ( 5 )$ when $f ( x ) = x - 7$ and $g ( x ) = 4 x + 1$

Accepted Answer

A)  $- \frac { 1 } { 10 }$ 
B)  $- \frac { 2 } { 25 }$ 
C)  $- \frac { 2 } { 21 }$ 
D)  $\frac { 1 } { 5 }$ 
A)  $- \frac { 1 } { 10 }$ 
B)  $- \frac { 2 } { 25 }$ 
C)  $- \frac { 2 } { 21 }$ 
D)  $\frac { 1 } { 5 }$

Question 20

Solve the problem.
-Suppose that a sales person observes that if an item is priced at $7 per item then 11 items are sold. If 9 items are sold for $9 per item then find a linear function f(x) = mx + b whose input is the price
Of the item in dollars and whose output is the number of items sold.

Accepted Answer

A)  f(x) = x + 18 
B)  f(x) = -x + 18 
C)  f(x) = -x + 4 
D)  f(x) = x + 4 
A)  f(x) = x + 18 
B)  f(x) = -x + 18 
C)  f(x) = -x + 4 
D)  f(x) = x + 4

Find the x- and y-intercepts. If no x-intercepts exist, state so. - $f ( x ) = 2 x ^ { 2 } - 4 x - 48$

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

Solve the problem. - $f ( x ) = ( x + 11 ) ^ { 2 } - 3 ( x \geq - 11 )$

For the given functions f(x) and g(x), find (f ∙ g)(x) or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f ( x ) = ( x + 3 ) ^ { 2 }$

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. - $f ( x ) = ( x - 6 ) ^ { 2 } + 11$

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. - $f ( x ) = - ( x - 2 ) ^ { 2 } + 5$

Given f(x) and g(x), find the indicated composition and state its domain. -For $f ( x ) = 5 \sqrt { x + 3 }$ and $g ( x ) = 2 x + 9$ , what is the domain of $g \circ f$ ?

Solve the problem. -A projectile is thrown upward so that its distance above the ground after t sec is given by $h ( t ) = - 13 t ^ { 2 } + 364 t$

Find the x- and y-intercepts. If no x-intercepts exist, state so. - $f ( x ) = 6 x ^ { 2 } + 12 x + 3$

Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2. -Shift 66 units to the left and 72 units down.

For the given function f(x), find f-1(x). - $f ( x ) = \frac { 3 x + 6 } { 6 x + 9 }$

Given f(x) and g(x), find the indicated composition and state its domain. -For $f ( x ) = 5 x - 5$ and $g ( x ) = 2 x + 5$ , what is the domain of $f \cdot g$ ?

For the given functions f(x) and g(x), find (f ∙ g)(x) or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f ( x ) = - 7 x + 4 , g ( x ) = 5 x ^ { 2 } - x + 5$ Find $( f \cdot g ) ( x )$ .

Solve the problem. -An electrician charges a fee of $45 plus $30 per hour. Find a linear function f(x) = mx + b whose input is the number of hours worked and whose output is the total cost of the job. Find the Slope-intercept form of the equation.

Given f(x) and g(x), find the indicated composition and state its domain. - $f ( x ) = 7 x + 10 , g ( x ) = 3 x - 1$ Find $( f \circ g ) ( x )$ .

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

Given f(x) and g(x), find the indicated composition and state its domain. -For $f ( x ) = \frac { 1 } { x - 7 }$ and $g ( x ) = \frac { 9 } { x }$ , what is the domain of $f \circ g$ ?

For the functions f(x) and g(x), evaluate the indicated function. -Find $\left( \frac { f } { g } \right) ( 5 )$ when $f ( x ) = x - 7$ and $g ( x ) = 4 x + 1$

Solve the problem. -Suppose that a sales person observes that if an item is priced at $7 per item then 11 items are sold. If 9 items are sold for $9 per item then find a linear function f(x) = mx + b whose input is the price Of the item in dollars and whose output is the number of items sold.

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

Find the x- and y-intercepts. If no x-intercepts exist, state so. - f(x)=2x2−4x−48f ( x ) = 2 x ^ { 2 } - 4 x - 48f(x)=2x2−4x−48

Find the vertex. - f(x)=−(x+2)2+5f ( x ) = - ( x + 2 ) ^ { 2 } + 5f(x)=−(x+2)2+5

Solve the problem. - f(x)=(x+11)2−3(x≥−11)f ( x ) = ( x + 11 ) ^ { 2 } - 3 ( x \geq - 11 )f(x)=(x+11)2−3(x≥−11)

For the given functions f(x) and g(x), find (f ∙ g)(x) or (fg)(x) \left(\frac{f}{g}\right)(x) (gf​)(x) as indicated. - f(x)=(x+3)2f ( x ) = ( x + 3 ) ^ { 2 }f(x)=(x+3)2

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+11f ( x ) = ( x - 6 ) ^ { 2 } + 11f(x)=(x−6)2+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)2+5f ( x ) = - ( x - 2 ) ^ { 2 } + 5f(x)=−(x−2)2+5

Given f(x) and g(x), find the indicated composition and state its domain. -For f(x)=5x+3f ( x ) = 5 \sqrt { x + 3 }f(x)=5x+3​ and g(x)=2x+9g ( x ) = 2 x + 9g(x)=2x+9 , what is the domain of g∘fg \circ fg∘f ?

Solve the problem. -A projectile is thrown upward so that its distance above the ground after t sec is given by h(t)=−13t2+364th ( t ) = - 13 t ^ { 2 } + 364 th(t)=−13t2+364t

Find the x- and y-intercepts. If no x-intercepts exist, state so. - f(x)=6x2+12x+3f ( x ) = 6 x ^ { 2 } + 12 x + 3f(x)=6x2+12x+3