Question 1

Determine whether or not the function is one-to-one.
-

Accepted Answer

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

Question 2

Solve the inequality.
-$x ^ { 2 } + 17 x < 0$

Accepted Answer

A)  $x  17$ 
B)  $- 17  0$ 
D)  $0 < x < 17$ 
A)  $x  17$ 
B)  $- 17  0$ 
D)  $0 < x < 17$

Question 3

The graph of  y=$\sqrt [ 3 ] { x }$  is shifted  3.5  units to the left. This graph is then vertically stretched by a factor of 5.1. Finally, the graph is reflected across the  x -axis.

Accepted Answer

A)  $y = - 5.1 \sqrt [ 3 ] { x - 3.5 }$ 
B)  $y = 5.1 \sqrt [ 3 ] { x + 3.5 }$ 
C)  $y = - 5.1 \sqrt [ 3 ] { x + 3.5 }$ 
D)  $y = - 3.5 \sqrt [ 3 ] { x + 5.1 }$ 
A)  $y = - 5.1 \sqrt [ 3 ] { x - 3.5 }$ 
B)  $y = 5.1 \sqrt [ 3 ] { x + 3.5 }$ 
C)  $y = - 5.1 \sqrt [ 3 ] { x + 3.5 }$ 
D)  $y = - 3.5 \sqrt [ 3 ] { x + 5.1 }$

Question 4

Determine whether or not the function is one-to-one.
-$f ( x ) = 4 x ^ { 2 } + x$

Accepted Answer

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

Question 5

The graph of  y= x3  is shifted  3.0  units to the right and then vertically compressed by a factor of  0.7 .

Accepted Answer

A)   y=3.0(x-0.7)3  
B)   y=0.7 x3+3.0 
C)   y=0.7(x+3.0)3 
D)   y=0.7(x-3.0)3 
A)   y=3.0(x-0.7)3  
B)   y=0.7 x3+3.0 
C)   y=0.7(x+3.0)3 
D)   y=0.7(x-3.0)3

Question 6

Use the quadratic formula or graphing methods to
-$$8 x ^ { 2 } - 36 x + 8 \leq 0$$

Accepted Answer

A)  $x \geq \frac { 9 + \sqrt { 65 } } { 4 } \approx 4.266$ 
B)  $\frac { 9 - \sqrt { 65 } } { 4 } \approx 0.234 \leq x \leq \frac { 9 + \sqrt { 65 } } { 4 } \approx 4.266$ 
C)  $x \leq \frac { 9 - \sqrt { 65 } } { 4 } \approx 0.234$ 
D)  $x \leq \frac { 9 - \sqrt { 65 } } { 4 } \approx 0.234$ or $x \geq \frac { 9 + \sqrt { 65 } } { 4 } \approx 4.266$ 
A)  $x \geq \frac { 9 + \sqrt { 65 } } { 4 } \approx 4.266$ 
B)  $\frac { 9 - \sqrt { 65 } } { 4 } \approx 0.234 \leq x \leq \frac { 9 + \sqrt { 65 } } { 4 } \approx 4.266$ 
C)  $x \leq \frac { 9 - \sqrt { 65 } } { 4 } \approx 0.234$ 
D)  $x \leq \frac { 9 - \sqrt { 65 } } { 4 } \approx 0.234$ or $x \geq \frac { 9 + \sqrt { 65 } } { 4 } \approx 4.266$

Question 7

The cost  C  of producing  t  units is given by $C ( t ) = 3 t ^ { 2 } + 7 t$ and the revenue  R  generated from selling  t  units is given by $R ( t ) = 4 t ^ { 2 } + t$. For what values of  t  will there be a profit?

Accepted Answer

A)  $t > 8$ 
B)  $t > 6$ 
C) $t > 0$ 
D)  $t > 7$ 
A)  $t > 8$ 
B)  $t > 6$ 
C) $t > 0$ 
D)  $t > 7$

Question 8

Determine if the function f defined by the set of ordered pairs has an inverse. If so, find the inverse.
- {(6,-7),(11,-6),(9,-5),(7,-4)}

Accepted Answer

A)   {(7,6),(6,11),(-5,9),(-4,7)} 
B)  No inverse 
C)   {(6,-7),(11,-6),(9,-5),(7,-4)} 
D)   {(-7,6),(-6,11),(-5,9),(-4,7)} 
A)   {(7,6),(6,11),(-5,9),(-4,7)} 
B)  No inverse 
C)   {(6,-7),(11,-6),(9,-5),(7,-4)} 
D)   {(-7,6),(-6,11),(-5,9),(-4,7)}

Question 9

Fill in each blank with the appropriate response.
-The graph of $y = | x - 4 | + 3$ can be obtained from the graph of $y = | x |$ by shifting horizontally ـــــــــunits to theـــــــــ , and shifting vertically ـــــــــــunits in theــــــــــــــ direction.

Accepted Answer

A)  3; right; 4 downward 
B)  3; right; 4; upward 
C)  4; right; 3; upward 
D)  4; left; 3; upward 
A)  3; right; 4 downward 
B)  3; right; 4; upward 
C)  4; right; 3; upward 
D)  4; left; 3; upward

Question 10

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

Question 11

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

Question 12

Solve the equation
-$\sqrt [ 3 ] { 3 x ^ { 2 } + 3 x - 1 } = \sqrt [ 3 ] { x }$

Accepted Answer

A)   x= $\frac { 1 } { 3 }$ 
B)   x=-1, x= $\frac { 1 } { 3 }$ 
C)   x=-1, x=-$\frac { 1 } { 3 }$ 
D)  No solution 
A)   x= $\frac { 1 } { 3 }$ 
B)   x=-1, x= $\frac { 1 } { 3 }$ 
C)   x=-1, x=-$\frac { 1 } { 3 }$ 
D)  No solution

Question 13

Solve the inequality.
-$8 m ^ { 2 } - 11 m > 0$

Accepted Answer

A)  $0  \frac { 11 } { 8 }$ 
C)  $- \frac { 11 } { 8 }  \frac { 11 } { 8 }$ 
A)  $0  \frac { 11 } { 8 }$ 
C)  $- \frac { 11 } { 8 }  \frac { 11 } { 8 }$

Question 14

Determine whether or not the function is one-to-one.
-$\{ ( 1,27 ) , ( 2,40 ) , ( 3,55 ) , ( 4,55 ) , ( 5,21 ) \}$

Accepted Answer

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

Question 15

Determine whether the function is even, odd, or neither.
-$y = | x - 4 |$

Accepted Answer

A)  Even 
B)  Neither 
C)  Odd 
A)  Even 
B)  Neither 
C)  Odd

Question 16

A coin is tossed upward from a balcony  390 ft  high (h0) with an initial velocity (v0) of  16 ft/sec , according to the formula $h ( t ) = - 16 t ^ { 2 } + v _ { 0 } t + h 0$. where  t  is time in seconds. During what interval of time will the coin be at a height of at least  70 ft ?

Accepted Answer

A)  $4 \sec \leq t \leq 5 \mathrm { sec }$ 
B)  $0 \mathrm { sec } \leq \mathrm { t } \leq 5 \mathrm { sec }$ 
C)  $5 \mathrm { sec } \leq \mathrm { t } \leq 10 \mathrm { sec }$ 
D)  $0 \sec \leq t \leq 1 \mathrm { sec }$ 
A)  $4 \sec \leq t \leq 5 \mathrm { sec }$ 
B)  $0 \mathrm { sec } \leq \mathrm { t } \leq 5 \mathrm { sec }$ 
C)  $5 \mathrm { sec } \leq \mathrm { t } \leq 10 \mathrm { sec }$ 
D)  $0 \sec \leq t \leq 1 \mathrm { sec }$

Question 17

The cost of manufacturing clocks is given by $C ( x ) = 72 + 62 x - x ^ { 2 }$. Also, it is known that in thours the number of clocks that can be produced is given by  x=9t , where $1 \leq t \leq 12$  Express C as a function of t .

Accepted Answer

A)   C(t)=72+62t-9 
B)   C(t)=72+558t-81t2 
C)   C(t)=72+62t+t2 
D)   C(t)=72+558t-81t 
A)   C(t)=72+62t-9 
B)   C(t)=72+558t-81t2 
C)   C(t)=72+62t+t2 
D)   C(t)=72+558t-81t

Question 18

Solve the equation
-$\sqrt { 8 x ^ { 2 } + 16 } - 3 x = 0$

Accepted Answer

A)   x=8 
B)  $x = \pm 5$ 
C)  $x = \pm 4$ 
D)   x=4 
A)   x=8 
B)  $x = \pm 5$ 
C)  $x = \pm 4$ 
D)   x=4

Question 19

For the pair of functions, perform the indicated operation.
-$f ( x ) = \frac { 5 x - 4 } { 3 } , g ( x ) = \frac { 1 } { x } \quad \text { Find } \left( \frac { f } { g } \right) ( x )$

Accepted Answer

A)  $\frac { 3 x } { 5 x - 4 }$ 
B)  $\frac { 3 } { 5 x ^ { 2 } - 4 x }$ 
C)  $\frac { 5 x ^ { 2 } - 4 x } { 3 }$ 
D)  $\frac { 5 x - 4 } { 3 x }$ 
A)  $\frac { 3 x } { 5 x - 4 }$ 
B)  $\frac { 3 } { 5 x ^ { 2 } - 4 x }$ 
C)  $\frac { 5 x ^ { 2 } - 4 x } { 3 }$ 
D)  $\frac { 5 x - 4 } { 3 x }$

Question 20

AAA Technology finds that the total revenue function associated with producing a new type of computer chip is  R(x)=70-0.3x2 , and the total cost function is  C(x)=6x+12 , where  x  represents the number of units of chips produced. Find the total profit function,  P(x) .

Accepted Answer

A)  $P ( x ) = - 0.03 x ^ { 2 } + 6 x - 58$ 
B)  $P ( x ) = - 0.03 x ^ { 2 } + 6 x + 82$ 
C)  $P ( x ) = - 0.03 x ^ { 2 } - 6 x + 58$ 
D)  $P ( x ) = 0.03 x ^ { 2 } + 6 x + 60$ 
A)  $P ( x ) = - 0.03 x ^ { 2 } + 6 x - 58$ 
B)  $P ( x ) = - 0.03 x ^ { 2 } + 6 x + 82$ 
C)  $P ( x ) = - 0.03 x ^ { 2 } - 6 x + 58$ 
D)  $P ( x ) = 0.03 x ^ { 2 } + 6 x + 60$

Determine whether or not the function is one-to-one. -

Solve the inequality. - $x ^ { 2 } + 17 x < 0$

The graph of y= $\sqrt [ 3 ] { x }$ is shifted 3.5 units to the left. This graph is then vertically stretched by a factor of 5.1. Finally, the graph is reflected across the x -axis.

Determine whether or not the function is one-to-one. - $f ( x ) = 4 x ^ { 2 } + x$

The graph of y= x³ is shifted 3.0 units to the right and then vertically compressed by a factor of 0.7 .

Use the quadratic formula or graphing methods to - $8 x ^ { 2 } - 36 x + 8 \leq 0$

The cost C of producing t units is given by $C ( t ) = 3 t ^ { 2 } + 7 t$ and the revenue R generated from selling t units is given by $R ( t ) = 4 t ^ { 2 } + t$ . For what values of t will there be a profit?

Determine if the function f defined by the set of ordered pairs has an inverse. If so, find the inverse. - {(6,-7),(11,-6),(9,-5),(7,-4)}

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

Solve the equation - $\sqrt [ 3 ] { 3 x ^ { 2 } + 3 x - 1 } = \sqrt [ 3 ] { x }$

Solve the inequality. - $8 m ^ { 2 } - 11 m > 0$

Determine whether or not the function is one-to-one. - $\{ ( 1,27 ) , ( 2,40 ) , ( 3,55 ) , ( 4,55 ) , ( 5,21 ) \}$

Determine whether the function is even, odd, or neither. - $y = | x - 4 |$

A coin is tossed upward from a balcony 390 ft high (h₀) with an initial velocity (v₀) of 16 ft/sec , according to the formula $h ( t ) = - 16 t ^ { 2 } + v _ { 0 } t + h 0$ . where t is time in seconds. During what interval of time will the coin be at a height of at least 70 ft ?

The cost of manufacturing clocks is given by $C ( x ) = 72 + 62 x - x ^ { 2 }$ . Also, it is known that in thours the number of clocks that can be produced is given by x=9t , where $1 \leq t \leq 12$ Express C as a function of t .

Solve the equation - $\sqrt { 8 x ^ { 2 } + 16 } - 3 x = 0$

For the pair of functions, perform the indicated operation. - $f ( x ) = \frac { 5 x - 4 } { 3 } , g ( x ) = \frac { 1 } { x } \quad \text { Find } \left( \frac { f } { g } \right) ( x )$

AAA Technology finds that the total revenue function associated with producing a new type of computer chip is R(x)=70-0.3x² , and the total cost function is C(x)=6x+12 , where x represents the number of units of chips produced. Find the total profit function, P(x) .

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

Determine whether or not the function is one-to-one. -

Solve the inequality. - x2+17x<0x ^ { 2 } + 17 x < 0x2+17x<0

The graph of y= x3\sqrt [ 3 ] { x }3x​ is shifted 3.5 units to the left. This graph is then vertically stretched by a factor of 5.1. Finally, the graph is reflected across the x -axis.

Determine whether or not the function is one-to-one. - f(x)=4x2+xf ( x ) = 4 x ^ { 2 } + xf(x)=4x2+x

The graph of y= x3 is shifted 3.0 units to the right and then vertically compressed by a factor of 0.7 .

Use the quadratic formula or graphing methods to - 8x2−36x+8≤08 x ^ { 2 } - 36 x + 8 \leq 08x2−36x+8≤0

The cost C of producing t units is given by C(t)=3t2+7tC ( t ) = 3 t ^ { 2 } + 7 tC(t)=3t2+7t and the revenue R generated from selling t units is given by R(t)=4t2+tR ( t ) = 4 t ^ { 2 } + tR(t)=4t2+t . For what values of t will there be a profit?