Question 1

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 + 11, g(x) = x - 2
Find (f ∙ g)(x).

Accepted Answer

A)  x2 - 22 
B)  x2 + 6x - 22 
C)  x2 + 9x - 22 
D)  x2 + 9x + 9 
A)  x2 - 22 
B)  x2 + 6x - 22 
C)  x2 + 9x - 22 
D)  x2 + 9x + 9

Question 2

Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2.
-Shift 4 units to the right.

Accepted Answer

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

Question 3

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 40 mph results in a rating of 32 mpg, where as at an
Average speed of 50 mph, her car rates 17 mpg. Find a linear function f(x) = mx + b whose input is The number of minutes for a call and whose output is the corresponding cost for the call. Use the Function to model the gas mileage y for an average speed of x mph.

Accepted Answer

A)  $f ( x ) = \frac { 2 } { 3 } x + 92$ 
B)  $f ( x ) = - \frac { 3 } { 2 } x + 92$ 
C)  $f ( x ) = - \frac { 3 } { 2 } x + 28$ 
D)  $f ( x ) = \frac { 2 } { 3 } x + 28$ 
A)  $f ( x ) = \frac { 2 } { 3 } x + 92$ 
B)  $f ( x ) = - \frac { 3 } { 2 } x + 92$ 
C)  $f ( x ) = - \frac { 3 } { 2 } x + 28$ 
D)  $f ( x ) = \frac { 2 } { 3 } x + 28$

Question 4

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

Accepted Answer

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

Question 5

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or
minimum value
-$$f ( x ) = 3 x ^ { 2 } - 18 x + 22$$

Accepted Answer

A)  Maximum, 3 
B)  Minimum, -5 
C)  Maximum, -5 
D)  Minimum, 3 
A)  Maximum, 3 
B)  Minimum, -5 
C)  Maximum, -5 
D)  Minimum, 3

Question 6

For the given functions f(x) and g(x), find (f ∙ g)(x) or $ \left(\frac{f}{g}\right)(x) $ as indicated.
-$$f ( x ) = 2 x ^ { 2 } + 2 x , g ( x ) = - 5 x ^ { 2 } - 15 x + 3$$
Find $( f - g ) ( x )$.

Accepted Answer

A)  $7 x ^ { 2 } - 13 x - 3$ 
B)  $24 x ^ { 2 } - 3$ 
C)  $- 3 x ^ { 2 } - 13 x + 3$ 
D)  $7 x ^ { 2 } + 17 x - 3$ 
A)  $7 x ^ { 2 } - 13 x - 3$ 
B)  $24 x ^ { 2 } - 3$ 
C)  $- 3 x ^ { 2 } - 13 x + 3$ 
D)  $7 x ^ { 2 } + 17 x - 3$

Question 7

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

Accepted Answer

A)  $5 x ^ { 4 } + 24 x ^ { 3 } + 38 x ^ { 2 } + 24 x + 8$ 
B)  $5 x ^ { 4 } + 20 x ^ { 3 } + 36 x ^ { 2 } + 24 x + 8$ 
C)  $5 x ^ { 4 } + 20 x ^ { 3 } + 38 x ^ { 2 } + 24 x + 8$ 
D)  $5 x ^ { 4 } + 24 x ^ { 3 } + 36 x ^ { 2 } + 24 x + 8$ 
A)  $5 x ^ { 4 } + 24 x ^ { 3 } + 38 x ^ { 2 } + 24 x + 8$ 
B)  $5 x ^ { 4 } + 20 x ^ { 3 } + 36 x ^ { 2 } + 24 x + 8$ 
C)  $5 x ^ { 4 } + 20 x ^ { 3 } + 38 x ^ { 2 } + 24 x + 8$ 
D)  $5 x ^ { 4 } + 24 x ^ { 3 } + 36 x ^ { 2 } + 24 x + 8$

Question 8

Find the x- and y-intercepts. If no x-intercepts exist, state so.
-$$f ( x ) = 6 x ^ { 2 } + 12 x + 1$$

Accepted Answer

A)  $\left( \frac { - 12 \pm \sqrt { 30 } } { 6 } , 0 \right) , ( 0,1 )$ 
B)  $\left( \frac { - 6 \pm \sqrt { 42 } } { 6 } , 0 \right) , ( 0 , - 1 )$ 
C)  $\left( \frac { - 6 \pm \sqrt { 30 } } { 12 } , 0 \right) , ( 0 , - 1 )$ 
D)  $\left\{ \frac { - 6 \pm \sqrt { 30 } } { 6 } , 0 , ( 0,1 ) \right.$ 
A)  $\left( \frac { - 12 \pm \sqrt { 30 } } { 6 } , 0 \right) , ( 0,1 )$ 
B)  $\left( \frac { - 6 \pm \sqrt { 42 } } { 6 } , 0 \right) , ( 0 , - 1 )$ 
C)  $\left( \frac { - 6 \pm \sqrt { 30 } } { 12 } , 0 \right) , ( 0 , - 1 )$ 
D)  $\left\{ \frac { - 6 \pm \sqrt { 30 } } { 6 } , 0 , ( 0,1 ) \right.$

Question 9

For the functions f(x) and g(x), evaluate the indicated function.
-Find $( f \cdot g ) ( 2 )$ when $f ( x ) = x - 4$ and $g ( x ) = - 4 x ^ { 2 } + 11 x + 5$

Accepted Answer

A)  $- 62$ 
B)  $- 66$ 
C)  $- 22$ 
D)  66 
A)  $- 62$ 
B)  $- 66$ 
C)  $- 22$ 
D)  66

Question 10

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

Accepted Answer

A)  right 2 units, down 6 units 
B)  rotate about x-axis, right 2 units, down 6 units 
C)  rotate about x-axis, left 2 units, down 6 units 
D)  left 2 units, down 6 units 
A)  right 2 units, down 6 units 
B)  rotate about x-axis, right 2 units, down 6 units 
C)  rotate about x-axis, left 2 units, down 6 units 
D)  left 2 units, down 6 units

Question 11

Solve the problem.
-$$f ( x ) = \sqrt { x - 5 } + 7$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = ( x + 5 ) ^ { 2 } - 7 , x \geq - 5$ 
B)  $f ^ { - 1 } ( x ) = x ^ { 2 } + 7 , x \geq 0$ 
C)  $f ^ { - 1 } ( x ) = ( x - 7 ) ^ { 2 } + 5 , x \geq 7$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = ( \mathrm { x } + 7 ) ^ { 2 } - 5 , \mathrm { x } \geq - 7$ 
A)  $f ^ { - 1 } ( x ) = ( x + 5 ) ^ { 2 } - 7 , x \geq - 5$ 
B)  $f ^ { - 1 } ( x ) = x ^ { 2 } + 7 , x \geq 0$ 
C)  $f ^ { - 1 } ( x ) = ( x - 7 ) ^ { 2 } + 5 , x \geq 7$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = ( \mathrm { x } + 7 ) ^ { 2 } - 5 , \mathrm { x } \geq - 7$

Question 12

For the given function f(x), find f-1(x).
-$$f ( x ) = \frac { 1 } { 3 } x + 7$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 3 \mathrm { x } - 21$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 7 } \mathrm { x } + 3$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 3 \mathrm { x } + 21$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 3 } x - 7$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 3 \mathrm { x } - 21$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 7 } \mathrm { x } + 3$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 3 \mathrm { x } + 21$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 3 } x - 7$

Question 13

For the given function f(x), find f-1(x).
-$$f ( x ) = \frac { 5 } { x + 8 }$$

Accepted Answer

A)  Not one-to-one 
B)  $f ^ { - 1 } ( x ) = \frac { 8 + 5 x } { x }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - 8 \mathrm { x } + 5 } { \mathrm { x } }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 8 + 5 \mathrm { x } }$ 
A)  Not one-to-one 
B)  $f ^ { - 1 } ( x ) = \frac { 8 + 5 x } { x }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - 8 \mathrm { x } + 5 } { \mathrm { x } }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 8 + 5 \mathrm { x } }$

Question 14

Given f(x) and g(x), find the indicated composition and evaluate.
-$$f ( x ) = 3 x + 9 ; g ( x ) = 6 x + 8$$
Find $( f \circ g ) ( 4 )$.

Accepted Answer

A)  672 
B)  134 
C)  53 
D)  105 
A)  672 
B)  134 
C)  53 
D)  105

Question 15

For the given function f(x), find f-1(x).
-f(x) = x + 6

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { x } { 6 }$ 
B)  $f ^ { - 1 } ( x ) = x - 6$ 
C)  $f ^ { - 1 } ( x ) = 6 - x$ 
D)  $f ^ { - 1 } ( x ) = - x + 6$ 
A)  $f ^ { - 1 } ( x ) = \frac { x } { 6 }$ 
B)  $f ^ { - 1 } ( x ) = x - 6$ 
C)  $f ^ { - 1 } ( x ) = 6 - x$ 
D)  $f ^ { - 1 } ( x ) = - x + 6$

Question 16

For the given function f(x), find f-1(x).
-$$f ( x ) = \frac { x - 10 } { x - 6 }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { x + 10 } { - 6 + x }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 6 x - 1 } { x - 10 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { - 6 x - 10 } { x - 1 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 6 \mathrm { x } - 10 } { \mathrm { x } - 1 }$ 
A)  $f ^ { - 1 } ( x ) = \frac { x + 10 } { - 6 + x }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 6 x - 1 } { x - 10 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { - 6 x - 10 } { x - 1 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 6 \mathrm { x } - 10 } { \mathrm { x } - 1 }$

Question 17

Given f(x) and g(x), find the indicated composition and state its domain.
-$$f ( x ) = \frac { x - 5 } { 9 } ; g ( x ) = 9 x + 5$$
Find $( g \circ f ) ( x )$.

Accepted Answer

A)  $x - \frac { 5 } { 9 }$, all real numbers 
B)  $x + 10$, all real numbers 
C)  $x$, all real numbers 
D)  $9 x + 40$, all real numbers 
A)  $x - \frac { 5 } { 9 }$, all real numbers 
B)  $x + 10$, all real numbers 
C)  $x$, all real numbers 
D)  $9 x + 40$, all real numbers

Question 18

Solve the problem.
-Suppose that a sales person observes that if an item is priced at $8 per item then 10 items are sold. Find a linear function f(x) = mx + b whose input is the number of hours that the plumber works
And whose output is the corresponding cost for the house call. If 8 items are sold for $10 per item
Then use the function to model the number y of items sold for x dollars per item.

Accepted Answer

A)  f(x) = x + 18 
B)  f(x) = -x + 18 
C)  f(x) = x + 2 
D)  f(x) = -x + 2 
A)  f(x) = x + 18 
B)  f(x) = -x + 18 
C)  f(x) = x + 2 
D)  f(x) = -x + 2

Question 19

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

Accepted Answer

A)  Domain: $( - \infty , \infty )$
 Range: $[ 4 , \infty )$ 
B)  Domain: $[ - 4 , \infty )$
Range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , \infty )$
Range: $[ - 4 , \infty )$ 
D)  Domain: $( - \infty , \infty )$
Range: $( - \infty , \infty )$ 
A)  Domain: $( - \infty , \infty )$
 Range: $[ 4 , \infty )$ 
B)  Domain: $[ - 4 , \infty )$
Range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , \infty )$
Range: $[ - 4 , \infty )$ 
D)  Domain: $( - \infty , \infty )$
Range: $( - \infty , \infty )$

Question 20

For the given function f(x), find f-1(x).
-$$f ( x ) = - 2 x$$

Accepted Answer

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

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 + 11, g(x) = x - 2 Find (f ∙ g)(x).

Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2. -Shift 4 units to the right.

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

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value - $f ( x ) = 3 x ^ { 2 } - 18 x + 22$

For the given functions f(x) and g(x), find (f ∙ g)(x) or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f ( x ) = 2 x ^ { 2 } + 2 x , g ( x ) = - 5 x ^ { 2 } - 15 x + 3$ Find $( f - g ) ( x )$ .

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

Find the x- and y-intercepts. If no x-intercepts exist, state so. - $f ( x ) = 6 x ^ { 2 } + 12 x + 1$

For the functions f(x) and g(x), evaluate the indicated function. -Find $( f \cdot g ) ( 2 )$ when $f ( x ) = x - 4$ and $g ( x ) = - 4 x ^ { 2 } + 11 x + 5$

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

Solve the problem. - $f ( x ) = \sqrt { x - 5 } + 7$

For the given function f(x), find f-1(x). - $f ( x ) = \frac { 1 } { 3 } x + 7$

For the given function f(x), find f-1(x). - $f ( x ) = \frac { 5 } { x + 8 }$

Given f(x) and g(x), find the indicated composition and evaluate. - $f ( x ) = 3 x + 9 ; g ( x ) = 6 x + 8$ Find $( f \circ g ) ( 4 )$ .

For the given function f(x), find f-1(x). -f(x) = x + 6

For the given function f(x), find f-1(x). - $f ( x ) = \frac { x - 10 } { x - 6 }$

Given f(x) and g(x), find the indicated composition and state its domain. - $f ( x ) = \frac { x - 5 } { 9 } ; g ( x ) = 9 x + 5$ Find $( g \circ f ) ( x )$ .

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

For the given function f(x), find f-1(x). - $f ( x ) = - 2 x$

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

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 + 11, g(x) = x - 2 Find (f ∙ g)(x).

Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2. -Shift 4 units to the right.

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

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value - f(x)=3x2−18x+22f ( x ) = 3 x ^ { 2 } - 18 x + 22f(x)=3x2−18x+22

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)=2x2+2x,g(x)=−5x2−15x+3f ( x ) = 2 x ^ { 2 } + 2 x , g ( x ) = - 5 x ^ { 2 } - 15 x + 3f(x)=2x2+2x,g(x)=−5x2−15x+3 Find (f−g)(x)( f - g ) ( x )(f−g)(x) .

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)=5x2+4x+2,g(x)=x2+4x+4f ( x ) = 5 x ^ { 2 } + 4 x + 2 , g ( x ) = x ^ { 2 } + 4 x + 4f(x)=5x2+4x+2,g(x)=x2+4x+4 Find (f⋅g)(x)( f \cdot g ) ( x )(f⋅g)(x) .

Find the x- and y-intercepts. If no x-intercepts exist, state so. - f(x)=6x2+12x+1f ( x ) = 6 x ^ { 2 } + 12 x + 1f(x)=6x2+12x+1

For the functions f(x) and g(x), evaluate the indicated function. -Find (f⋅g)(2)( f \cdot g ) ( 2 )(f⋅g)(2) when f(x)=x−4f ( x ) = x - 4f(x)=x−4 and g(x)=−4x2+11x+5g ( x ) = - 4 x ^ { 2 } + 11 x + 5g(x)=−4x2+11x+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−2)2−6f ( x ) = - ( x - 2 ) ^ { 2 } - 6f(x)=−(x−2)2−6

Solve the problem. - f(x)=x−5+7f ( x ) = \sqrt { x - 5 } + 7f(x)=x−5​+7

For the given function f(x), find f-1(x). - f(x)=13x+7f ( x ) = \frac { 1 } { 3 } x + 7f(x)=31​x+7

For the given function f(x), find f-1(x). - f(x)=5x+8f ( x ) = \frac { 5 } { x + 8 }f(x)=x+85​

Given f(x) and g(x), find the indicated composition and evaluate. - f(x)=3x+9;g(x)=6x+8f ( x ) = 3 x + 9 ; g ( x ) = 6 x + 8f(x)=3x+9;g(x)=6x+8 Find (f∘g)(4)( f \circ g ) ( 4 )(f∘g)(4) .