Question 1

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

Accepted Answer

A)  Yes 
B)  No

Question 2

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

Accepted Answer

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

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

Question 4

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

Accepted Answer

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

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 $x \geq \frac { 9 + \sqrt { 65 } } { 4 } \approx 4.266$

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)  $t > 7$

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)}

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

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)

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)  $y = ( x - 4 ) ^ { 2 } + 1$

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

Question 13

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

Accepted Answer

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

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

Question 15

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

Accepted Answer

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)  $0 \sec \leq t \leq 1 \mathrm { sec }$

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

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

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)  $\frac { 5 x - 4 } { 3 x }$

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)  $P ( x ) = 0.03 x ^ { 2 } + 6 x + 60$

Exam 4: Additional Topics With Functions

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) }

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) .

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?

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) }

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. -

Write the equation of the function g(x) that is transformed from the given function f(x) , and whose graph is shown. - f(x) =x2f(x) =x^{2}f(x) =x2

Solve the equation - 3x2+3x−13=x3\sqrt [ 3 ] { 3 x ^ { 2 } + 3 x - 1 } = \sqrt [ 3 ] { x }33x2+3x−1​=3x​

Solve the inequality. - 8m2−11m>08 m ^ { 2 } - 11 m > 08m2−11m>0

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

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

The cost of manufacturing clocks is given by C(x) =72+62x−x2C ( x ) = 72 + 62 x - x ^ { 2 }C(x) =72+62x−x2 . Also, it is known that in thours the number of clocks that can be produced is given by x=9t , where 1≤t≤121 \leq t \leq 121≤t≤12 Express C as a function of t .

Solve the equation - 8x2+16−3x=0\sqrt { 8 x ^ { 2 } + 16 } - 3 x = 08x2+16​−3x=0

For the pair of functions, perform the indicated operation. - f(x) =5x−43,g(x) =1x Find (fg) (x) f ( x ) = \frac { 5 x - 4 } { 3 } , g ( x ) = \frac { 1 } { x } \quad \text { Find } \left( \frac { f } { g } \right) ( x ) f(x) =35x−4​,g(x) =x1​ Find (gf​) (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) .