Question 1

Determine if the complete graph represents a function that is even, odd, or neither.
-

Accepted Answer

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

Question 2

Find the specified domain and express it in interval notation.
-If  f(x)=x2  and  g(x)=2-x , evaluate  (f-g)(3)

Accepted Answer

A)  10 
B)   -9 
C)  4 
D)  0 
A)  10 
B)   -9 
C)  4 
D)  0

Question 3

The function that models the consumption of a certain medication over the years  2000-2010  is  f(x)=115.21x+224.10 , where x  is the number of years after 2000 and  y  is measured in grams per 100,000 people. Find the inverse of this function.

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 115.21 } - 224.10$ 
B)  $f ^ { - 1 } ( x ) = \frac { 1 } { 115.21 x + 224.10 }$ 
C)  $f ^ { - 1 } ( x ) = 115.21 ( x - 224.10 )$ 
D)  $f ^ { - 1 } ( x ) = \frac { x - 224.10 } { 115.21 }$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 115.21 } - 224.10$ 
B)  $f ^ { - 1 } ( x ) = \frac { 1 } { 115.21 x + 224.10 }$ 
C)  $f ^ { - 1 } ( x ) = 115.21 ( x - 224.10 )$ 
D)  $f ^ { - 1 } ( x ) = \frac { x - 224.10 } { 115.21 }$

Question 4

Solve the equation
-$x ^ { 2 / 3 } - 5 x ^ { 1 / 3 } + 6 = 0$

Accepted Answer

A)   -27,-8 
B)  2,3 
C)  8,27 
D)   -3,-2 
A)   -27,-8 
B)  2,3 
C)  8,27 
D)   -3,-2

Question 5

Find the inverse of the function.
-$$f ( x ) = \sqrt { x + 3 }$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = ( \mathrm { x } + 3 ) ^ { 2 }$ 
B)  $f ^ { - 1 } ( x ) = x ^ { 2 } - 3 , x \geq 0$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { x - 3 }$ 
D)  Not a one-to-one function 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = ( \mathrm { x } + 3 ) ^ { 2 }$ 
B)  $f ^ { - 1 } ( x ) = x ^ { 2 } - 3 , x \geq 0$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { x - 3 }$ 
D)  Not a one-to-one function

Question 6

For the pair of functions, perform the indicated operation.
-$f ( x ) = x ^ { 3 } + 3 x ^ { 2 } , g ( x ) = \sqrt { x - 8 }$ Find  (f+g)(x) .

Accepted Answer

A)  $x ^ { 3 } + \sqrt { 3 x ^ { 2 } + x - 8 }$ 
B)  $\sqrt { x ^ { 3 } + 3 x ^ { 2 } + x - 8 }$ 
C)  $x ^ { 3 } + 3 x ^ { 2 } + \sqrt { x - 8 }$ 
D)  $x ^ { 3 } + 3 x ^ { 2 } + x - 8$ 
A)  $x ^ { 3 } + \sqrt { 3 x ^ { 2 } + x - 8 }$ 
B)  $\sqrt { x ^ { 3 } + 3 x ^ { 2 } + x - 8 }$ 
C)  $x ^ { 3 } + 3 x ^ { 2 } + \sqrt { x - 8 }$ 
D)  $x ^ { 3 } + 3 x ^ { 2 } + x - 8$

Question 7

The graph of the function y $y = f ( x ) \text { is given. On the same axes, sketch the graph of } f ^ { - 1 } ( x )$ . Use a dashed line for the inverse
function.
-

Accepted Answer

A) 
  
B) 
$\text { Function is its own inverse. }$
  
C) 
  
D) 
  
A) 
  
B) 
$\text { Function is its own inverse. }$
  
C) 
  
D)

Question 8

Find the specified domain and express it in interval notation.
-For $f ( x ) = 2 x - 5$ and $g ( x ) = \sqrt { x + 8 }$, what is the domain of $\left( \frac { f } { g } \right) ( x )$ ?

Accepted Answer

A)  $[ 0 , \infty )$ 
B)  $( - 8 , \infty )$ 
C)  $( - 8,8 )$ 
D)  $[ 8 , \infty )$ 
A)  $[ 0 , \infty )$ 
B)  $( - 8 , \infty )$ 
C)  $( - 8,8 )$ 
D)  $[ 8 , \infty )$

Question 9

At Allied Electronics, production has begun on the  X-15  Computer Chip. The total revenue function is given by $R ( x ) = 52 x - 0.3 x ^ { 2 }$ and the total cost function is given by  C(x)=2 x+8 , where  x  represents the number of boxes of computer chips produced. The total profit function,  P(x) , is such that  P(x)=R(x)-C(x) . Find  P(x) .

Accepted Answer

A)  $P ( x ) = - 0.3 x ^ { 2 } + 48 x + 8$ 
B)  $P ( x ) = 0.3 x ^ { 2 } + 48 x - 24$ 
C)  $P ( x ) = - 0.3 x ^ { 2 } + 50 x - 8$ 
D)  $P ( x ) = 0.3 x ^ { 2 } + 50 x - 16$ 
A)  $P ( x ) = - 0.3 x ^ { 2 } + 48 x + 8$ 
B)  $P ( x ) = 0.3 x ^ { 2 } + 48 x - 24$ 
C)  $P ( x ) = - 0.3 x ^ { 2 } + 50 x - 8$ 
D)  $P ( x ) = 0.3 x ^ { 2 } + 50 x - 16$

Question 10

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.
-$y = - 4 x ^ { 3 } + 6 x$

Accepted Answer

A)   x -axis 
B)   x -axis,  y -axis 
C)   x -axis, origin 
D)  Origin 
A)   x -axis 
B)   x -axis,  y -axis 
C)   x -axis, origin 
D)  Origin

Question 11

Solve the inequality.
-$x ^ { 2 } - 6 x \geq - 8$

Accepted Answer

A)  $x \geq 4$ 
B)  $x \leq 2 \text { or } x \geq 4$ 
C)  $x \leq 2$ 
D)  $2 \leq x \leq 4$ 
A)  $x \geq 4$ 
B)  $x \leq 2 \text { or } x \geq 4$ 
C)  $x \leq 2$ 
D)  $2 \leq x \leq 4$

Question 12

Provide an appropriate response.
-Why does a quadratic function never have an inverse?

Accepted Answer

Quadratic functions are of the form @#LAT-DLM&. Tw

Question 13

Determine if the function f defined by the arrow diagram has an inverse. If it does, create an arrow diagram that defines
the inverse. If not, explain why not.
-

Accepted Answer

A)  Yes; 
B)  No; the function is not one-to-one
  
A)  Yes; 
B)  No; the function is not one-to-one

Question 14

Find the requested composition of functions.
-Given $f ( x ) = 4 x ^ { 2 } + 3 x + 5 \text { and } g ( x ) = 3 x - 4 \text {, find } ( g \circ f ) ( x )$

Accepted Answer

A)   12x2+9 x+19 
B)   4x2+9 x+11 
C)   12x2+9 x+11 
D)   4x2+3 x+1 
A)   12x2+9 x+19 
B)   4x2+9 x+11 
C)   12x2+9 x+11 
D)   4x2+3 x+1

Question 15

Determine the values of x for which f(x) and g(x) are inverse functions.
-$$f ( x ) = - x ^ { 2 } + 16 , g ( x ) = \sqrt { 16 - x }$$

Accepted Answer

A)  $x \leq 16$ 
B)  $x \geq 16$ 
C)  $x \leq 0$ 
D)  $x \geq 0$ 
A)  $x \leq 16$ 
B)  $x \geq 16$ 
C)  $x \leq 0$ 
D)  $x \geq 0$

Question 16

Write the equation of the graph after the indicated transformation(s).
-The graph of $y = x ^ { 2 }$ is shifted 3 units to the left. This graph is then vertically compressed by a factor of $\frac { 1 } { 5 }$ and reflected across the $x$-axis. Finally, the graph is shifted 7 units downward.

Accepted Answer

A)  $y = \frac { 1 } { 5 } ( x - 3 ) ^ { 2 } - 7$ 
B)  $y = - \frac { 1 } { 5 } ( x - 3 ) ^ { 2 } - 7$ 
C)  $y = - \frac { 1 } { 5 } ( x - 3 ) ^ { 2 } + 7$ 
D)  $y = - \frac { 1 } { 5 } ( x + 3 ) ^ { 2 } - 7$ 
A)  $y = \frac { 1 } { 5 } ( x - 3 ) ^ { 2 } - 7$ 
B)  $y = - \frac { 1 } { 5 } ( x - 3 ) ^ { 2 } - 7$ 
C)  $y = - \frac { 1 } { 5 } ( x - 3 ) ^ { 2 } + 7$ 
D)  $y = - \frac { 1 } { 5 } ( x + 3 ) ^ { 2 } - 7$

Question 17

Solve the equation
-$\sqrt [ 3 ] { 3 x - 1 } = \sqrt [ 3 ] { 4 x + 1 }$

Accepted Answer

A)   x=-2 
B)   x=-$\frac { 2 } { 3 }$ 
C)   x=0 
D)   x=2 
A)   x=-2 
B)   x=-$\frac { 2 } { 3 }$ 
C)   x=0 
D)   x=2

Question 18

For the functions f and g, find the requested value.
-$\text { Evaluate } ( g \circ f ) ( ) \text {. }$
$y=f(x)$

$y=g(x)$

Accepted Answer

A)   -1 
B)   -3 
C)   -4 
D)   -2 
A)   -1 
B)   -3 
C)   -4 
D)   -2

Question 19

Solve the inequality.
-$x ^ { 2 } - 2 x - 24 \leq 0$

Accepted Answer

A)  $- 4 \leq x \leq 6$ 
B)  $x \geq 6$ 
C)  $x \leq - 4 \text { or } x \geq 6$ 
D)  $x \leq - 4$ 
A)  $- 4 \leq x \leq 6$ 
B)  $x \geq 6$ 
C)  $x \leq - 4 \text { or } x \geq 6$ 
D)  $x \leq - 4$

Question 20

For the pair of functions, perform the indicated operation.
-$f ( x ) = 7 - 7 x , g ( x ) = - 5 x ^ { 2 } + 7 \quad \text { Find } ( f + g ) ( x )$

Accepted Answer

A)  $- 12 x ^ { 2 } - 7 x + 14$ 
B)  $- 5 x ^ { 2 } + 7$ 
C)  $- 5 x ^ { 2 } - 7 x + 14$ 
D)   -12 x+14 
A)  $- 12 x ^ { 2 } - 7 x + 14$ 
B)  $- 5 x ^ { 2 } + 7$ 
C)  $- 5 x ^ { 2 } - 7 x + 14$ 
D)   -12 x+14

Determine if the complete graph represents a function that is even, odd, or neither. -

Find the specified domain and express it in interval notation. -If f(x)=x² and g(x)=2-x , evaluate (f-g)(3)

The function that models the consumption of a certain medication over the years 2000-2010 is f(x)=115.21x+224.10 , where x is the number of years after 2000 and y is measured in grams per 100,000 people. Find the inverse of this function.

Solve the equation - $x ^ { 2 / 3 } - 5 x ^ { 1 / 3 } + 6 = 0$

Find the inverse of the function. - $f ( x ) = \sqrt { x + 3 }$

For the pair of functions, perform the indicated operation. - $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } , g ( x ) = \sqrt { x - 8 }$ Find (f+g)(x) .

Find the specified domain and express it in interval notation. -For $f ( x ) = 2 x - 5$ and $g ( x ) = \sqrt { x + 8 }$ , what is the domain of $\left( \frac { f } { g } \right) ( x )$ ?

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - $y = - 4 x ^ { 3 } + 6 x$

Solve the inequality. - $x ^ { 2 } - 6 x \geq - 8$

Provide an appropriate response. -Why does a quadratic function never have an inverse?

Determine if the function f defined by the arrow diagram has an inverse. If it does, create an arrow diagram that defines the inverse. If not, explain why not. -

Find the requested composition of functions. -Given $f ( x ) = 4 x ^ { 2 } + 3 x + 5 \text { and } g ( x ) = 3 x - 4 \text {, find } ( g \circ f ) ( x )$

Determine the values of x for which f(x) and g(x) are inverse functions. - $f ( x ) = - x ^ { 2 } + 16 , g ( x ) = \sqrt { 16 - x }$

Write the equation of the graph after the indicated transformation(s). -The graph of $y = x ^ { 2 }$ is shifted 3 units to the left. This graph is then vertically compressed by a factor of $\frac { 1 } { 5 }$ and reflected across the $x$ -axis. Finally, the graph is shifted 7 units downward.

Solve the equation - $\sqrt [ 3 ] { 3 x - 1 } = \sqrt [ 3 ] { 4 x + 1 }$

Solve the inequality. - $x ^ { 2 } - 2 x - 24 \leq 0$

For the pair of functions, perform the indicated operation. - $f ( x ) = 7 - 7 x , g ( x ) = - 5 x ^ { 2 } + 7 \quad \text { Find } ( f + g ) ( x )$

Functions, Graphs, and Models; Linear Functions

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Quadratic, Piecewise-Defined, and Power Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

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Exam 4: Additional Topics With Functions

Determine if the complete graph represents a function that is even, odd, or neither. -

Find the specified domain and express it in interval notation. -If f(x)=x2 and g(x)=2-x , evaluate (f-g)(3)

The function that models the consumption of a certain medication over the years 2000-2010 is f(x)=115.21x+224.10 , where x is the number of years after 2000 and y is measured in grams per 100,000 people. Find the inverse of this function.

Solve the equation - x2/3−5x1/3+6=0x ^ { 2 / 3 } - 5 x ^ { 1 / 3 } + 6 = 0x2/3−5x1/3+6=0

Find the inverse of the function. - f(x)=x+3f ( x ) = \sqrt { x + 3 }f(x)=x+3​

For the pair of functions, perform the indicated operation. - f(x)=x3+3x2,g(x)=x−8f ( x ) = x ^ { 3 } + 3 x ^ { 2 } , g ( x ) = \sqrt { x - 8 }f(x)=x3+3x2,g(x)=x−8​ Find (f+g)(x) .

The graph of the function y y=f(x) is given. On the same axes, sketch the graph of f−1(x)y = f ( x ) \text { is given. On the same axes, sketch the graph of } f ^ { - 1 } ( x )y=f(x) is given. On the same axes, sketch the graph of f−1(x) . Use a dashed line for the inverse function. -

Find the specified domain and express it in interval notation. -For f(x)=2x−5f ( x ) = 2 x - 5f(x)=2x−5 and g(x)=x+8g ( x ) = \sqrt { x + 8 }g(x)=x+8​ , what is the domain of (fg)(x)\left( \frac { f } { g } \right) ( x )(gf​)(x) ?

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - y=−4x3+6xy = - 4 x ^ { 3 } + 6 xy=−4x3+6x

Solve the inequality. - x2−6x≥−8x ^ { 2 } - 6 x \geq - 8x2−6x≥−8