Question 1

Find and simplify  for the function.
​

Accepted Answer

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

Question 2

Evaluate h (7), where  ​  ,  ​

Accepted Answer

The answer of Evaluate h (7), where  ​ ...

Question 3

Evaluate  , where  ​  ,  ​  __________

Accepted Answer

The answer of Evaluate  , where  ​ ...

Question 4

If f and g are functions, then  .
​

Accepted Answer

The statement is too vague and requires more information. It is not clear what the mathematical operation or relationship between f and g is, so it is impossible to determine the truth value of the statement.

Question 5

Find function  such that  ,  , and  . ​

Accepted Answer

The answer of Find function  such that  ,...

Question 6

Find function f such that  ,  , and  . ​

Accepted Answer

The given input strings have a pattern where the only changing variable is the third section from the end (6981, 6982, 6983). Therefore, to find the output, we need to find a pattern for the third section from the end. 
Observing the answer choices, we can see that the third section from the end is increasing by 1 in each choice. Therefore, the next number in the sequence should be 6984. 
Hence, the correct answer is C) 11eb651f_cb9e_6986_b0a1_c9bd5a9d4cd4_TB8255_11.

Question 7

Find the rules for the composite functions  and  ​  ,  ​

Accepted Answer

The answer of Find the rules for the composite functions...

Question 8

Let  and  . Find the rule for the function  . ​

Accepted Answer

The given function has only one different character in the first group of characters as compared to the two given examples. Therefore, the rule for the function should be such that the first group of characters remains the same as that in the second example ('11eb651f_cb9c_1f3c_b0a1_c3a11c343ce2_TB8255_11') but the 12th character (from the left) changes from 'c' to 'd'. The only option that fits this rule is C i.e. '11eb651f_cb9c_1f40_b0a1_2b9481677355_TB8255_11'.

Question 9

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

f(t) represents the number of IBM shares that Nancy owns at time t and g(t) represents the price per share of IBM stock at time t. Therefore, f(t)g(t) represents the value in dollars of Nancy's shares of IBM at time t, as it is the product of the number of shares and their corresponding price per share.

Question 10

Evaluate h (3), where  ​  ,  ​

Accepted Answer

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

Question 11

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  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 12

Find the functions  ​  ,  ​

Accepted Answer

The answer of Find the functions  ​  ,...

Question 13

Find function  such that  ,  , and  . ​

Accepted Answer

The answer of Find function  such that  ,...

Question 14

Evaluate  , where  ​  ,  ​
Round the answer to two decimal places, if necessary
​  __________

Accepted Answer

The answer of Evaluate  , where  ​ ...

Question 15

Find  for the function. Simplify your answer.
​

Accepted Answer

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

Question 16

Let  ,  . Find the rule for the function  . ​

Accepted Answer

The answer of Let  ,  . Find the...

Question 17

TMI, a manufacturer of blank audiocassette tapes, has a monthly fixed cost of $10,500 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 answer of TMI, a manufacturer of blank audiocassette tapes,...

Question 18

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

Accepted Answer

Looking at the given function and the three examples, it appears that the function is creating a sequential pattern by increasing the last set of characters in each value by 1.

- The first example is 11eb651f_cb9c_4653_b0a1_4b28e0c3fca5_TB8255_11. The last set of characters is TB8255_11. 
- The second example is 11eb651f_cb9c_4654_b0a1_d945002e3b54_TB8255_11. The last set of characters is TB8255_11, which is the same as the first example, but with the last two characters increased by 1. 
- The third example is 11eb651f_cb9c_4655_b0a1_17f9cdd50c11_TB8255_11. The last set of characters is TB8255_11, which is the same as the first example, but with the last two characters increased by 2.

Therefore, to continue this pattern, the fourth example should have the last set of characters as TB8255_11 but with the last two characters increased by 3. Only choice C matches this pattern, which means the answer is C.

Question 19

Let  ,  . Find the rule for the function  . ​

Accepted Answer

The answer of Let  ,  . Find the...

Question 20

Find  for the function  . Simplify your answer. ​

Accepted Answer

The answer of Find  for the function  ....

Quiz 2: Functions, Limits, and the Derivative

Find and simplify for the function.

Evaluate h (7) , where ,

Evaluate , where , __________

If f and g are functions, then .

Find function such that , , and .

Find function f such that , , and .

Find the rules for the composite functions and ,

Let and . Find the rule for the function .

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?

Evaluate h (3) , where ,

Find the functions ,

Find function such that , , and .

Evaluate , where , Round the answer to two decimal places, if necessary __________

Find for the function. Simplify your answer.

Let , . Find the rule for the function .

TMI, a manufacturer of blank audiocassette tapes, has a monthly fixed cost of $10,500 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.

Let , and . Find the rule for the function .

Let , . Find the rule for the function .

Find for the function . Simplify your answer.

Quiz 2: Functions, Limits, and the Derivative

Find and simplify for the function. ​

Evaluate h (7) , where ​ , ​

Evaluate , where ​ , ​ __________

If f and g are functions, then . ​

Find function such that , , and . ​

Find function f such that , , and . ​

Find the rules for the composite functions and ​ , ​

Let and . Find the rule for the function . ​

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? ​

Evaluate h (3) , where ​ , ​

Find the functions ​ , ​

Find function such that , , and . ​

Evaluate , where ​ , ​ Round the answer to two decimal places, if necessary ​ __________

Find for the function. Simplify your answer. ​

Let , . Find the rule for the function . ​

TMI, a manufacturer of blank audiocassette tapes, has a monthly fixed cost of $10,500 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. ​

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

Let , . Find the rule for the function . ​

Find for the function . Simplify your answer. ​

Find and simplify for the function.

Evaluate h (7) , where ,

Evaluate , where , __________

If f and g are functions, then .

Find function such that , , and .

Find function f such that , , and .

Find the rules for the composite functions and ,

Let and . Find the rule for the function .

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?

Evaluate h (3) , where ,

Find the functions ,

Find function such that , , and .

Evaluate , where , Round the answer to two decimal places, if necessary __________

Find for the function. Simplify your answer.

Let , . Find the rule for the function .

TMI, a manufacturer of blank audiocassette tapes, has a monthly fixed cost of $10,500 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.

Let , and . Find the rule for the function .

Let , . Find the rule for the function .

Find for the function . Simplify your answer.