Question 1

Solve the problem.&#10;Bob owns a watch repair shop. He has found that the cost of operating his shop is given by

Accepted Answer

To find the minimum cost, we need to find the value of $x$ that minimizes the function $c(x)$. This can be done by finding the derivative of $c(x)$ and setting it equal to 0:

$$c'(x) = 4x - 200 = 0 \implies x = 50$$

Therefore, Bob must repair 50 watches to have the lowest cost.

Question 2

Given f(x) and g(x), find the indicated composition and state its domain.&#10;

Accepted Answer

To find $(g \circ f)(x)$, substitute $f(x)$ into $g(x)$: $g(f(x)) = 9\left(\frac{x - 5}{9}\right) + 5$. Simplifying this gives $x - 5 + 5 = x$, so the composition is $x$, and its domain is all real numbers because there are no restrictions on $x$.

Question 3

Given f(x) and g(x), find the indicated composition and state its domain.&#10;

Accepted Answer

To find the composition of f(x) and g(x), we need to substitute the expression for g(x) into the expression for f(x):
$$f(g(x))=5(2x+5)-5=10x+20$$
The domain of f(x) is all real numbers and the domain of g(x) is all real numbers. The domain of the composition f(g(x)) will be all real numbers because we can input any real number into g(x) and get a real number out, which can then be input into f(x) to get another real number out. Therefore, the answer is (B) $(-\infty, \infty)$.

Note: The question asks for the composition $f\cdot g$, which typically means multiplication. However, based on the context and the answer choices, it is clear that the question is actually asking for the composition $f(g(x))$ and not the product $f(x)g(x)$.

Question 4

Given f(x) and g(x), find the indicated composition and state its domain.&#10;

Accepted Answer

The domain of $f \cdot g$ is determined by the domain of $f(g(x))$, which requires $g(x) + 2 \geq 0$. Given $g(x) = 4x + 10$, we solve $4x + 10 + 2 \geq 0$ leading to $4x + 12 \geq 0$ or $x \geq -3$. Thus, the domain is $[ - 3 , \infty )$.

Question 5

Given f(x) and g(x), find the indicated composition and state its domain.&#10;

Accepted Answer

To find the composition, we first have to substitute f(x) into g(x), so we get:
$$g(f(x)) = 2(5\sqrt{x+3})+9 = 10\sqrt{x+3}+9$$
Now we need to consider the domain of g(f(x)) which is restricted by the domain of f(x). The expression inside the square root of f(x) must be non-negative, since we cannot take the square root of a negative number. Hence, we have:
$$x+3 \geq 0 \implies x\geq -3$$
Therefore, the domain of g(f(x)) is $[-3, \infty)$. The correct answer is D.

Question 6

Given f(x) and g(x), find the indicated composition and state its domain.&#10;

Accepted Answer

To find the domain of $f \circ g$, we need to find the values of x for which $g(x)$ is in the domain of $f(x)$. 
The domain of $g(x)$ is $(-\infty,\infty)$. 
Now, we need to find the values of x for which $g(x)$ is not in the domain of $f(x)$. 
$g(x)$ is not in the domain of $f(x)$ if and only if $g(x)=0$ (since the denominator of $f(x)$ must be nonzero). 
Thus, we need to solve the equation $\frac{4}{(2-x)^6}=0$. This equation has no real solutions. 
Therefore, the domain of $f \circ g$ is $(-\infty,2)\cup(2,\infty)$.

Note: It's important to also check if there are any other values of x for which $g(x)$ is not in the domain of $f(x)$, such as when the denominator of $g(x)$ is zero. However, in this case, the domain of $g(x)$ is already $(-\infty,\infty)$, so there are no such values.

Question 7

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or&#10;minimum value&#10; &#10;A) Maximum, 1&#10;B) Minimum, 1&#10;C) Maximum, 9&#10;D) Minimum, 9

Accepted Answer

The quadratic function $f(x) = 2x^2 - 4x + 11$ is in the form $ax^2 + bx + c$, where $a = 2$, $b = -4$, and $c = 11$. Since $a > 0$, the parabola opens upwards, indicating a minimum value. To find the minimum value, use the vertex formula $x = -\frac{b}{2a}$ to find the x-coordinate of the vertex. Substituting $a = 2$ and $b = -4$ gives $x = -\frac{-4}{2*2} = 1$. Then, substitute $x = 1$ into the original equation to find the minimum value: $f(1) = 2(1)^2 - 4(1) + 11 = 2 - 4 + 11 = 9$.

Question 8

Given f(x) and g(x), find the indicated composition and state its domain.&#10;

Accepted Answer

The composition of $h$ and $g$ is $h \cdot g ( x ) = h ( g ( x ) ) = h \left( \sqrt { x + 4 } \right) = \frac{1}{\sqrt{x+4}-7}$.

Now, we need to find the domain of $h \cdot g$. Since the denominator of $h \cdot g$ is $\sqrt{x+4}-7$, we need to make sure that this expression does not equal zero.

Thus, we get $\sqrt{x+4}-7 \neq 0$, which implies that $\sqrt{x+4} \neq 7$. Squaring both sides gives us $x+4 \neq 49$, so $x \neq 45$.

Therefore, the domain of $h \cdot g$ is $[ -4,45 ) \cup ( 45 , \infty )$.

The correct choice is C.

Question 9

Given f(x) and g(x), find the indicated composition and state its domain.&#10;

Accepted Answer

To find the composition of $f \circ g$, we need to substitute the expression for g(x) into f(x) wherever we see x in f(x). Hence, 
$$(f \circ g)(x) = f(g(x)) = f\left(\frac{9}{x}\right) = \frac{1}{\frac{9}{x} - 7}.$$ 
Simplifying this expression, we get 
$$(f \circ g)(x) = \frac{-x}{9x-63}.$$
The domain of $(f \circ g)(x)$ consists of all values of x for which the expression inside the fraction is defined and not equal to zero ($\frac{1}{0}$ is undefined). Solving $9x-63 \neq 0$ gives us $x \neq 7$. Therefore, the domain of $(f \circ g)(x)$ is given by
$$( - \infty , 0 ) \cup \left( 0 , \frac { 9 } { 7 } \right) \cup \left( \frac { 9 } { 7 } , \infty \right),$$
which is the same as choice D.

Question 10

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or
minimum value

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

Accepted Answer

The quadratic function $f(x) = 3x^2 - 18x + 22$ has a positive leading coefficient (3), indicating it opens upwards and thus has a minimum value. The vertex form reveals the minimum value, calculated as $-\frac{b}{2a}$ for x, and substituting back into the function gives the minimum value of -5.

Question 11

Given f(x) and g(x), find the indicated composition and state its domain.&#10;

Accepted Answer

The answer of Given f(x) and g(x), find the indicated...

Question 12

Given f(x) and g(x), find the indicated composition and state its domain.&#10;

Accepted Answer

The answer of Given f(x) and g(x), find the indicated...

Question 13

Given f(x) and g(x), find the indicated composition and state its domain.&#10;

Accepted Answer

The answer of Given f(x) and g(x), find the indicated...

Question 14

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 15

Solve the problem.&#10;A projectile is thrown upward so that its distance above the ground after t sec is given by  &#10;A) 21 sec&#10;B) 14 sec&#10;C) 28 sec&#10;D) 7 sec

Accepted Answer

The answer of Solve the problem.&#10;A projectile is thrown upward...

Question 16

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or
minimum value

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

Accepted Answer

The answer of Determine whether the given quadratic function has...

Question 17

Given f(x) and g(x), find the indicated composition and state its domain.&#10;

Accepted Answer

The answer of Given f(x) and g(x), find the indicated...

Question 18

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or
minimum value

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

Accepted Answer

The answer of Determine whether the given quadratic function has...

Question 19

Given f(x) and g(x), find the indicated composition and state its domain.&#10;

Accepted Answer

The answer of Given f(x) and g(x), find the indicated...

Question 20

Given f(x) and g(x), find the indicated composition and state its domain.&#10;

Accepted Answer

The answer of Given f(x) and g(x), find the indicated...

Question 21

For the given function f(x), find f-1(x).&#10;f(x) = x + 6

Accepted Answer

The answer of For the given function f(x), find f-1(x).&#10;f(x)...

Question 22

For the given function f(x), find f-1(x).&#10;

Accepted Answer

The answer of For the given function f(x), find f-1(x).&#10;...

Question 23

Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2.&#10;

Accepted Answer

The answer of Determine a quadratic function that results when...

Question 24

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 25

Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2.&#10;Shift 66 units to the left and 72 units down.

Accepted Answer

The answer of Determine a quadratic function that results when...

Question 26

Solve the problem.&#10;What is the minimum product of two numbers whose difference is 84?&#10;A) -3528&#10;B) -21&#10;C) -42&#10;D) -1764

Accepted Answer

The answer of Solve the problem.&#10;What is the minimum product...

Question 27

Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2.&#10;

Accepted Answer

The answer of Determine a quadratic function that results when...

Question 28

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 29

For the given function f(x), find f-1(x).&#10;f(x) = 8x

Accepted Answer

The answer of For the given function f(x), find f-1(x).&#10;f(x)...

Question 30

Solve the problem.&#10; &#10;A) 20 in.&#10;B) 400 in.&#10;C) 0 in.&#10;D) 10 in.

Accepted Answer

The answer of Solve the problem.&#10; &#10;A) 20 in.&#10;B) 400...

Question 31

For the given function f(x), find f-1(x).&#10;

Accepted Answer

The answer of For the given function f(x), find f-1(x).&#10;...

Question 32

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 33

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 34

Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2.&#10;

Accepted Answer

The answer of Determine a quadratic function that results when...

Question 35

Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2.&#10;

Accepted Answer

The answer of Determine a quadratic function that results when...

Question 36

For the given function f(x), find f-1(x).&#10;

Accepted Answer

The answer of For the given function f(x), find f-1(x).&#10;...

Question 37

For the given function f(x), find f-1(x).&#10;

Accepted Answer

The answer of For the given function f(x), find f-1(x).&#10;...

Question 38

Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2.&#10;

Accepted Answer

The answer of Determine a quadratic function that results when...

Question 39

Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2.&#10;Shift 7 units to the left.

Accepted Answer

The answer of Determine a quadratic function that results when...

Question 40

For the given function f(x), find f-1(x).&#10;f(x) = 5 - x

Accepted Answer

The answer of For the given function f(x), find f-1(x).&#10;f(x)...

Question 41

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.

A) down 8 units
B) left 8 units
C) up 8 units
D) right 8 units

Accepted Answer

The answer of Without graphing the function, state the shift(s)...

Question 42

For the given function f(x), find f-1(x). State the domain of f-1(x).&#10;

Accepted Answer

The answer of For the given function f(x), find f-1(x)....

Question 43

For the given function f(x), find f-1(x).&#10;

Accepted Answer

The answer of For the given function f(x), find f-1(x).&#10;...

Question 44

For the given function f(x), find f-1(x). State the domain of f-1(x).&#10;

Accepted Answer

The answer of For the given function f(x), find f-1(x)....

Question 45

For the given function f(x), find f-1(x). State the domain of f-1(x).
It costs $800 to start up a business of selling hot dogs. Each hot dog costs $0.60 to produce. Find the cost function C(x) = mx + b whose input is the number of hot dogs and whose output is the total
Cost. Use this function to find the cost of producing 300 hot dogs?

A) $18,800
B) $180
C) $980
D) $860

Accepted Answer

The answer of For the given function f(x), find f-1(x)....

Question 46

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.

A) down 8 units
B) left 8 units
C) up 8 units
D) right 8 units

Accepted Answer

The answer of Without graphing the function, state the shift(s)...

Question 47

For the given function f(x), find f-1(x). State the domain of f-1(x).&#10;

Accepted Answer

The answer of For the given function f(x), find f-1(x)....

Question 48

For the given function f(x), find f-1(x). State the domain of f-1(x).&#10;

Accepted Answer

The answer of For the given function f(x), find f-1(x)....

Question 49

For the given function f(x), find f-1(x). State the domain of f-1(x).
It costs $800 to start up a business of selling hot dogs. Each hot dog costs $0.60 to produce. Find the cost function C(x) = mx + b whose input is the number of hot dogs and whose output is the total
Cost. Use this function to find the cost of producing 300 hot dogs?

A) $18,800
B) $180
C) $980
D) $860

Accepted Answer

The answer of For the given function f(x), find f-1(x)....

Question 50

For the given function f(x), find f-1(x). State the domain of f-1(x).
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

The answer of For the given function f(x), find f-1(x)....

Question 51

For the given function f(x), find f-1(x). State the domain of f-1(x).&#10;

Accepted Answer

The answer of For the given function f(x), find f-1(x)....

Question 52

For the given function f(x), find f-1(x).&#10;

Accepted Answer

The answer of For the given function f(x), find f-1(x).&#10;...

Question 53

For the given function f(x), find f-1(x).&#10;

Accepted Answer

The answer of For the given function f(x), find f-1(x).&#10;...

Question 54

For the given function f(x), find f-1(x). State the domain of f-1(x).
It costs $800 to start up a business of selling hot dogs. Each hot dog costs $0.60 to produce. Find the cost function C(x) = mx + b whose input is the number of hot dogs and whose output is the total
Cost. Use this function to find the cost of producing 300 hot dogs?

A) $18,800
B) $180
C) $980
D) $860

Accepted Answer

The answer of For the given function f(x), find f-1(x)....

Question 55

For the given function f(x), find f-1(x). State the domain of f-1(x).
It costs $800 to start up a business of selling hot dogs. Each hot dog costs $0.60 to produce. Find the cost function C(x) = mx + b whose input is the number of hot dogs and whose output is the total
Cost. Use this function to find the cost of producing 300 hot dogs?

A) $18,800
B) $180
C) $980
D) $860

Accepted Answer

The answer of For the given function f(x), find f-1(x)....

Question 56

For the given function f(x), find f-1(x). State the domain of f-1(x).&#10;

Accepted Answer

The answer of For the given function f(x), find f-1(x)....

Question 57

For the given function f(x), find f-1(x). State the domain of f-1(x).
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

The answer of For the given function f(x), find f-1(x)....

Question 58

For the given function f(x), find f-1(x). State the domain of f-1(x).
It costs $800 to start up a business of selling hot dogs. Each hot dog costs $0.60 to produce. Find the cost function C(x) = mx + b whose input is the number of hot dogs and whose output is the total
Cost. Use this function to find the cost of producing 300 hot dogs?

A) $18,800
B) $180
C) $980
D) $860

Accepted Answer

The answer of For the given function f(x), find f-1(x)....

Question 59

For the given function f(x), find f-1(x). State the domain of f-1(x).
It costs $800 to start up a business of selling hot dogs. Each hot dog costs $0.60 to produce. Find the cost function C(x) = mx + b whose input is the number of hot dogs and whose output is the total
Cost. Use this function to find the cost of producing 300 hot dogs?

A) $18,800
B) $180
C) $980
D) $860

Accepted Answer

The answer of For the given function f(x), find f-1(x)....

Question 60

For the given function f(x), find f-1(x). State the domain of f-1(x).&#10;

Accepted Answer

The answer of For the given function f(x), find f-1(x)....

Question 61

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.

A) down 8 units
B) left 8 units
C) up 8 units
D) right 8 units

Accepted Answer

The answer of Without graphing the function, state the shift(s)...

Question 62

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.

A) down 8 units
B) left 8 units
C) up 8 units
D) right 8 units