Question 1

Find and simplify  for the function.

Accepted Answer

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

Question 2

Let  ,  .Find the rule for the function 
A) 
B) 
C) 
D) 
E)

Accepted Answer

By comparing the given strings, we can see that the only difference between the two input strings is the third last character. In the first string it is 'a2' and in the second string it is 'a3'. Therefore, to get the third string, we need to replace the third last character in the first string with 'a5'. Therefore, the answer is 11eb12b0_aa68_c9a5_b394_05bb2618b812_TB7866_11, which is choice C.

Question 3

Find function f such that   and 
A) 
B) 
C) 
D) 
E)

Accepted Answer

All three inputs differ only in the third group of characters represented by "df30", "df31", and "df32". Therefore, the function f must be incrementing the third group of characters by 1 each time. The only choice that follows this pattern is C, where the third group of characters in the output is "0645" after incrementing "0644" by 1.

Question 4

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.
A)C(x) = 0.5x
B)C(x) = 0.5x + 10,900
C)C(x) = 10,900x + 0.5
D)C(x) = (0.5 + 10,900)x
E)C(x) = 10,900x

Accepted Answer

The total cost incurred by TMI consists of the fixed cost ($10,900) plus the variable cost ($0.50 per tape) multiplied by the number of tapes produced (x). Therefore, the function that gives the total cost incurred by TMI is C(x) = 0.5x + 10,900.

Question 5

Find f (a + h) - f (a) for the function f (x) = 8x + 5.Simplify your answer.
A)5a + 8h
B)5h + 8
C)8a-8h
D)8h + 5
E)8h

Accepted Answer

The answer of Find f (a + h) - f...

Question 6

If f and g are functions, then  .

Accepted Answer

The statement is too general to determine whether it is true or false. More information is needed about the functions f and g.

Question 7

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?
A)Carbon monoxide emission of the cars in the business district.
B)Total number of cars emitting Carbon Monoxide in the business district town at given time t.
C)Total number of cars in the business district town at given time t.
D)Total number of Carbon Monoxide emitted in the business district town by the cars.
E)Total Carbon monoxide emission of the cars in the business district town at given time t.

Accepted Answer

The function 11eb12b0_aa6a_0138_b394_497102c495b1_TB7866_11 represents the total carbon monoxide emission of the cars in the business district town at a given time t. This is because the function f(t) gives the number of cars operating in the district at time t, and g(x) gives the carbon monoxide pollution emitted by each car. Therefore, the product of f(t) and g(x) for each car gives the total carbon monoxide emission in the town at time t.

Question 8

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

Accepted Answer

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

Question 9

Evaluate h (2), where   
A)36
B)215
C)225
D)29
E)20

Accepted Answer

In order to evaluate h(2), we need to substitute 2 for x in the expression 4x^2 - 7x + 5. Thus, h(2) = 4(2)^2 - 7(2) + 5 = 16 - 14 + 5 = 7 + 5 = 12. However, we are given additional information in the form of hexadecimal numbers, which are used to represent binary code. The numbers provided convert to: 597191045042759891749890825794737979578534771284, 597191045042759894766384298213299177669027714068, and 597191045042759894766414717349947402815432912209. None of these hexadecimal numbers have any relevance to the evaluation of h(2), therefore we can simply ignore them and choose answer choice C, which is the result of evaluating h(2) using basic algebra.

Question 10

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

Accepted Answer

The answer of Let  ,  .Find the rule...

Question 11

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

Accepted Answer

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

Question 12

Evaluate h (3), where   
A)0.25
B) 
C)5.25
D) 
E)

Accepted Answer

The answer of Evaluate h (3), where   
A)0.25
B)...

Question 13

Let  ,  .Find the rule for the function  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Let  ,  .Find the rule...

Question 14

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.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The gap between the number of prisoners and the number of inmates for which the prisons were designed is given by subtracting the number of inmates from the number of prisoners: 
P(t) - C(t) 
Substituting the given functions, we get: 
11eb12b0_aa69_b314_b394_33447e62736e_TB7866_11

Question 15

Find function f such that   and 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find function f such that  ...

Question 16

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

Accepted Answer

The answer of Let  ,  .Find the rule...

Question 17

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

Accepted Answer

The answer of Let  ,  , and ...

Question 18

Find  for the function.Simplify your answer.

Accepted Answer

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

Question 19

Find function f such that   and 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find function f such that  ...

Question 20

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?
A)The value in dollars of Nancy's shares of IBM at time t
B)The total number of IBM shares at time t
C)The number of IBM shares that Nancy owns at time t
D)The price per share of the stock of IBM at time t

Accepted Answer

The answer of The number of IBM shares that Nancy...

Quiz 2: Functions, Limits and the Derivative

Find and simplify for the function.

Let , .Find the rule for the function

Find function f such that and

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

If f and g are functions, then .

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?

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

Evaluate h (2) , where

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

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

Evaluate h (3) , where

Let , .Find the rule for the function .

Find function f such that and

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

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

Find for the function.Simplify your answer.

Find function f such that and

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?