Question 1

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 2

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 3

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

Accepted Answer

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

Question 4

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 5

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

Accepted Answer

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

Question 6

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 7

Find function f such that   and

Accepted Answer

The answer of Find function f such that  ...

Question 8

Find the rules for the composite functions  and

Accepted Answer

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

Question 9

Let   and  .Find the rule for the function

Accepted Answer

The answer of Let   and  .Find the...

Question 10

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

Plugging in -6 into x and -12 into y, we have:

y = 11e^(-x/6)

y = 11e^(-(-6)/6)=11e^(1)

y = 11e

y ≠ -12

Therefore, the point (-6,-12) does not lie on the graph of the function.

Question 11

Find function f such that   and

Accepted Answer

The answer of Find function f such that  ...

Question 12

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 13

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 14

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...

Question 15

Find function f such that   and

Accepted Answer

The answer of Find function f such that  ...

Question 16

Let  ,  .Find the rule for the function

Accepted Answer

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

Question 17

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

B)

C)

D)

E)

Accepted Answer

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

Question 18

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 19

Let  and  .Find the rule for the function  .

Accepted Answer

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

Question 20

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

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

Quiz 2: Functions, Limits and the Derivative

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.

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

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

Let f be the function defined by Find and

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

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

Let and .Find the rule for the function

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

Find function f such that and

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.

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?

Find function f such that and

Let , .Find the rule for the function

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

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

Let and .Find the rule for the function .

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