Question 1

If f and g are functions, then  . Answer true or false.

Accepted Answer

The answer of If f and g are functions, then...

Question 2

Refer to the graph of the function f in the following figure.  Find the value of x for which (i) f (x) = 3 and (ii) f (x) = 0.
A) f (3) = 3, f (2) = 0
B) f (4) = 3, f (3) = 0
C) f (4) = 3, f (2) = 0
D) f (3) = 3, f (1) = 0
E) f (3) = 5, f (0) = -2

Accepted Answer

The answer of Refer to the graph of the function...

Question 3

Determine whether the point (- 6, - 12) lies on the graph of the function 
A) Yes, the point lies on the graph.
B) No, the point does not lie on the graph.

Accepted Answer

The given function is not specified in the question. Without the function, we cannot determine if the point (-6,-12) lies on its graph or not. Therefore, it is not possible to make a valid choice for this question.

Question 4

Let  ,  . Find the rule for the function

Accepted Answer

The answer of Let  ,  . Find the...

Question 5

Let f be the function defined by f (x) = 3x + 9. Find     and 
A)

B)

C)

D)

E)

Accepted Answer

To find the values of the function at the given inputs, we simply substitute them in the function and simplify.

f(0) = 3(0) + 9 = 9
f(1) = 3(1) + 9 = 12
f(2) = 3(2) + 9 = 15
f(3) = 3(3) + 9 = 18
f(4) = 3(4) + 9 = 21

These values correspond to the answer choices B.

Question 6

Let h be the function defined by  . Find h(8), h(0), h(a) and h(  a).
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Let h be the function defined by...

Question 7

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 8

Let   and  . Find the rule for the function

Accepted Answer

The answer of Let   and  . Find...

Question 9

Find the functions f + g, f - g, fg, and

Accepted Answer

The answer of Find the functions f + g, f...

Question 10

Let f be the function defined by  Find    and 
A)

B)

C)

D)

E)

Accepted Answer

The answer of Let f be the function defined by...

Question 11

Find function f such that   and

Accepted Answer

The answer of Find function f such that  ...

Question 12

Find f (a + h) - f (a) for the function f (x) = 2x + 4. Simplify your answer.

Accepted Answer

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

Question 13

Find function f such that   and

Accepted Answer

The answer of Find function f such that  ...

Question 14

Find the rules for the composite functions  and

Accepted Answer

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

Question 15

Find function f such that   and

Accepted Answer

The answer of Find function f such that  ...

Question 16

Let f be the function defined by  Find f (0), f (25), and f (50).
A) f (0) = 9, f (25) = 4, f (50) = - 1
B) f (0) = 29, f (25) = 4, f (50) = - 1
C) f (0) = 29, f (25) = 4, f (50) = - 25
D) f (0) = 4, f (25) =  , f (50) = - 1
E) f (0) = 9, f (25) =  , f (50) = - 25

Accepted Answer

The answer of Let f be the function defined by...

Question 17

TMI, a manufacturer of blank audiocassette tapes, has a monthly fixed cost of $13,100 and a variable cost of $0.40/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 f be the function defined by f (x) = 4x + 8. Find f (1), f (- 1), f (a), f (- a), and f (a + 1).
A) f (1) = 11, f (- 1) = 5, f (a) = 4a + 8, f(- a) = - 4a + 8
B) f (1) = 10, f (- 1) = 6, f (a) = 12, f(- a) = 4, f (a + 1) = 4a + 12
C) f (1) = 12, f (- 1) = 4, f (a) = a + 8, f(- a) = - a + 8, f (a + 1) = 4a + -4
D) f (1) = 12, f (- 1) = 4, f (a) = 4a + 8, f(- a) = - 4a + 8, f (a + 1) = 4a + 12
E) f (1) = 12, f (- 1) = 4, f (a) = 4a + 8, f(- a) = 4, f (a + 1) = 4a + 8

Accepted Answer

- f(1) = 4(1) + 8 = 12
- f(-1) = 4(-1) + 8 = 4
- f(a) = 4a + 8 (given in the function definition)
- f(-a) = 4(-a) + 8 = -4a + 8
- f(a+1) = 4(a+1) + 8 = 4a + 12.

Therefore, the correct choice is D, with all the options matching the correct answers.

Question 19

Find the domain of the function. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the domain of the function. 
A)...

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?

Accepted Answer

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

Quiz 2: Functions, Limits and the Derivative

If f and g are functions, then . Answer true or false.

Refer to the graph of the function f in the following figure. Find the value of x for which (i) f (x) = 3 and (ii) f (x) = 0.

Determine whether the point (- 6, - 12) lies on the graph of the function

Let , . Find the rule for the function

Let f be the function defined by f (x) = 3x + 9. Find and

Let h be the function defined by . Find h(8) , h(0) , h(a) and h( a) .

Let and . Find the rule for the function

Find the functions f + g, f - g, fg, and

Let f be the function defined by Find and

Find function f such that and

Find f (a + h) - f (a) for the function f (x) = 2x + 4. Simplify your answer.

Find function f such that and

Find the rules for the composite functions and

Find function f such that and

Let f be the function defined by Find f (0) , f (25) , and f (50) .

TMI, a manufacturer of blank audiocassette tapes, has a monthly fixed cost of $13,100 and a variable cost of $0.40/tape. Find a function C that gives the total cost incurred by TMI in the manufacture of x tapes/month.

Let f be the function defined by f (x) = 4x + 8. Find f (1) , f (- 1) , f (a) , f (- a) , and f (a + 1) .

Find the domain of 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?