Question 1

Let  ,  , and  Find the rule for the function fgh.

Accepted Answer

The answer of Let  ,  , and ...

Question 2

Let  ,  . Find the rule for the function

Accepted Answer

The answer of Let  ,  . Find the...

Question 3

The number of cars running in the business district of a town at time t is given by f (t). Carbon monoxide pollution coming from these cars is given by g(x) parts per million, where x is the number of cars being operated in the district. What does the function  represent?

Accepted Answer

The function 11eaa8b1_dca9_6c52_b1b6_fb375ffa5336_TB6026_11 represents the total Carbon monoxide emission from the cars in the business district town at a given time t, as it is a function of the number of cars emitting Carbon Monoxide (x), which is then multiplied by g(x) parts per million. Therefore, the correct choice is E.

Question 4

Find function f such that   and

Accepted Answer

Looking at the given inputs, it can be observed that the only difference among them is in the third pair of digits (aa, 38db, 38dc). Also, the options provided have the same format, where the only changing digit is in the third pair of digits. 
Thus, we can conclude that the function f is adding 1 to the third pair of digits in the input value to generate the output value. 
So, applying the same function to the third input value (38dc + 1 = 38dd), we get the output value 11eaa8b1_dca6_38dd_b1b6_2b47a789f883_TB6026_11, which matches with option C. Therefore, option C is the correct answer.

Question 5

Evaluate h (2), where    h (2) = __________

Accepted Answer

The answer of Evaluate h (2), where   ...

Question 6

The number of IBM shares that Nancy owns is given by f (t). The price per share of the stock of IBM at time t is g(t) dollars. What does the function f (t)g(t) represent?

Accepted Answer

The function f(t) represents the number of IBM shares that Nancy owns at time t, and g(t) represents the price per share of the stock of IBM at time t. Therefore, f(t)g(t) represents the value in dollars of Nancy's shares of IBM at time t.

Question 7

TMI, a manufacturer of blank audiocassette tapes, has a monthly fixed cost of $10,900 and a variable cost of $0.50/tape. Find a function C that gives the total cost incurred by TMI in the manufacture of x tapes/month.

Accepted Answer

The total cost incurred by TMI is the sum of the fixed cost and the variable cost. The variable cost is calculated as the cost per tape multiplied by the number of tapes produced.
So, we have:
Total Cost = Fixed Cost + Variable Cost
Variable Cost = Cost per Tape x Number of Tapes
Variable Cost = 0.5x
Fixed Cost = $10,900
Total Cost = 0.5x + $10,900
Therefore, the function that gives the total cost incurred by TMI in the manufacture of x tapes/month is C(x) = 0.5x + $10,900, which is option B.

Question 8

Find and simplify  for the function.

Accepted Answer

The answer of Find and simplify  for the function....

Question 9

Let  and  . Find the rule for the function  .

Accepted Answer

The answer of Let  and  . Find the...

Question 10

The 1980s saw a trend toward old-fashioned punitive deterrence as opposed to the more liberal penal policies and community-based corrections popular in the 1960s and early 1970s. As a result, prisons became more crowded, and the gap between the number of people in prison and the prison capacity widened. The number of prisoners (in thousands) in federal and state prisons is approximated by the function  where t is measured in years, with t = 0 corresponding to 1983. The number of inmates for which prisons were designed is given by  where C(t) is measured in thousands and t has the same meaning as before. Find an expression that shows the gap between the number of prisoners and the number of inmates for which the prisons were designed at any time t.

Accepted Answer

The answer of The 1980s saw a trend toward old-fashioned...

Question 11

Let  ,  . Find the rule for the function f - g.

Accepted Answer

The answer of Let  ,  . Find the...

Question 12

Find  for the function. Simplify your answer.

Accepted Answer

The answer of Find  for the function. Simplify your...

Question 13

Find function f such that   and

Accepted Answer

The answer of Find function f such that  ...

Question 14

Find f (a + h) - f (a) for the function f (x) = 8x + 5. Simplify your answer.

Accepted Answer

The expression f(a + h) - f(a) for f(x) = 8x + 5 is calculated as follows: f(a + h) = 8(a + h) + 5 = 8a + 8h + 5 and f(a) = 8a + 5. Subtracting these gives (8a + 8h + 5) - (8a + 5) = 8h.

Question 15

Evaluate h (3), where

Accepted Answer

The answer of Evaluate h (3), where   
...

Question 16

Let  ,  . Find the rule for the function  .

Accepted Answer

The answer of Let  ,  . Find the...

Question 17

Find function f such that   and

Accepted Answer

The answer of Find function f such that  ...

Question 18

If f and g are functions, then  .

Accepted Answer

The given statement is not necessarily true. The product of two functions f and g can be undefined if the codomain of g does not intersect with the domain of f. For example, if f(x) = 1/x and g(x) = x when x is not equal to zero and g(x) = 2 when x = 0, then f(x) * g(x) is undefined at x = 0.

Question 19

Let  ,  . Find the rule for the function f + g.

Accepted Answer

The answer of Let  ,  . Find the...

Question 20

Evaluate h (3), where    Round the answer to two decimal places, if necessary
h (3) = __________

Accepted Answer

The answer of Evaluate h (3), where   ...

Quiz 2: Functions, Limits and the Derivative

Let , , and Find the rule for the function fgh.

Let , . Find the rule for the function

The number of cars running in the business district of a town at time t is given by f (t) . Carbon monoxide pollution coming from these cars is given by g(x) parts per million, where x is the number of cars being operated in the district. What does the function represent?

Find function f such that and

Evaluate h (2), where h (2) = __________

The number of IBM shares that Nancy owns is given by f (t) . The price per share of the stock of IBM at time t is g(t) dollars. What does the function f (t) g(t) represent?

TMI, a manufacturer of blank audiocassette tapes, has a monthly fixed cost of $10,900 and a variable cost of $0.50/tape. Find a function C that gives the total cost incurred by TMI in the manufacture of x tapes/month.

Find and simplify for the function.

Let and . Find the rule for the function .

Let , . Find the rule for the function f - g.

Find for the function. Simplify your answer.

Find function f such that and

Find f (a + h) - f (a) for the function f (x) = 8x + 5. Simplify your answer.

Evaluate h (3) , where

Let , . Find the rule for the function .

Find function f such that and

If f and g are functions, then .

Let , . Find the rule for the function f + g.

Evaluate h (3), where Round the answer to two decimal places, if necessary h (3) = __________