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Axler- Precalculus: A Prelude to Calculus 2/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 19 / 19

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving...  ()

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1 2 3 4 5 6 7 8 9 10 11
–/1 –/1 –/1 –/1 –/3 –/1 –/2 –/1 –/6 –/1 –/1
Total
19/19 (100.0%)

  • Instructions

    Precalculus: A Prelude to Calculus by Sheldon Axler, published by John Wiley & Sons, Inc. is now a WebAssignPLUS selection. WebAssignPLUS includes a complete on-line version of the text and a variety of interactive study aids. All of these rich resources are linked together in a dynamic and interactive environment for students. Additional links to the eBook and GO Tutorials within each problem are structured to support the way students work and provide them with superior just-in-time learning resources. Also the eBook availability provides students with a significantly less expensive option than the printed version.

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1. –/1 points AxlerPreCalc2 1.1.005. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Assume
f(x) = 
x + 3
x2 + 1
 for every real number x. Evaluate and simplify the following expression.
f(4a) =

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2. –/1 points AxlerPreCalc2 1.1.028. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
The U. S. 2011 federal income tax for a single person with taxable income x dollars (this is the net income after allowable deductions and exemptions) is
g(x)
 dollars, where g is the function defined by federal law as follows:
g(x) = 
0.1x    if 0 ≤ x ≤ 8500
0.15x − 425    if 8500 < x ≤ 34,500
0.25x − 3875    if 34,500 < x ≤ 83,600
0.28x − 6383    if 83,600 < x ≤ 174,400
0.33x − 15,103    if 174,400 < x ≤ 379,150
0.35x − 22,686    if 379,150 < x.
Find the 2011 federal income tax for a single person whose taxable income that year was $140,000.
$

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3. –/1 points AxlerPreCalc2 1.1.058. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Select all the functions (displayed as tables) whose domain is
{0, 5, 8}
 and whose range is
{6, 7}.
 (Select all that apply.)
x
f(x)
6
 		0
6
 		5
7 8
        
x
f(x)
6
 		0
7 5
7 8
        
x
f(x)
0 6
5
7
8 7
              
x
f(x)
0
 		6
5 7
8 6
        
x
f(x)
0 7
5
6
8 6
        
x
f(x)
0
7
5 7
8 6
              
x
f(x)
6
0
7 8
        
x
f(x)
0 7
5 6
8 7
        
x f(x)
0 6
5 6
8
7

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4. –/1 points AxlerPreCalc2 1.2.020. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Assume f is the function with domain
[−4, 4]
 whose graph is shown below.
WebAssign Plot
Estimate the value of
f(3).

f(3) =

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5. –/3 points AxlerPreCalc2 1.3.024. My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
0/50 0/50 0/50
Total
–/3
 
Assume f is a function whose domain is the interval
[1, 5],
 whose range is the interval
[1, 3],
 and whose graph is the figure below.
WebAssign Plot
For the function
g(x) = f(x − 3),
 find the following.
(a) Find the domain of g. (Enter your answer using interval notation.)


(b) Find the range of g. (Enter your answer using interval notation.)


(c) Sketch the graph of g.

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6. –/1 points AxlerPreCalc2 1.3.060. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Suppose that to provide additional funds for higher education, the federal government adopts a new income tax plan that consists of the 2011 income tax plus an additional $700 per taxpayer. Let g be the function such that
g(x)
 is the 2011 federal income tax for a single person with taxable income x dollars, and let h be the corresponding function for the new income tax plan.

Write a formula for
h(x)
 in terms of
g(x).
    

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7. –/2 points AxlerPreCalc2 1.4.042. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/50 0/50
Total
–/2
 
Suppose
h(t) = 
t2 + 7
t − 7
 − 1
3
 
.
(a) If
g(t) = 
t2 + 7
t − 7
 − 1,
 then find a function f such that
h = f∘g.

f(t) =


(b) If
g(t) = 
t2 + 7
t − 7
,
 then find a function f such that
h = f∘g.

f(t) =

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8. –/1 points AxlerPreCalc2 1.4.057. My Notes
Question Part
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1
–/1
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Total
–/1
 
Suppose you are exchanging currency in the London airport. The currency exchange service there only makes transactions in which one of the two currencies is British pounds, but you want to exchange dollars for Euros. Thus you first need to exchange dollars for British pounds, then exchange British pounds for Euros. At the time you want to make the exchange, the function f for exchanging dollars for British pounds is given by the formula
f(d) = 0.66d − 3
and the function g for exchanging British pounds for Euros is given by the formula
g(p) = 1.23p − 4.
The subtraction of
3
 or
4
 in the number of British pounds or Euros that you receive is the fee charged by the currency exchange service for each transaction.

How many Euros would you receive for exchanging $100 after going through this two-step exchange process? (Round your answer to two decimal places.)
Euros

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9. –/6 points AxlerPreCalc2 1.5.021. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6
–/1 –/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50 0/50
Total
–/6
 
For the function
f(x) = 
10x  if x < 0
20x  if x ≥ 0
,
 find the following.
(a) Find the domain of f. (Enter your answer using interval notation.)


(b) Find the range of f. (Enter your answer using interval notation.)


(c) Find a formula for
f −1(y).
 You can check your solution by verifying that
f −1∘f = I
 and
f∘f −1 = I
 (recall that I is the function defined by
I(x) = x).

f −1(y) = 
 if y < 0
 if y ≥ 0


(d) Find the domain of
f −1(y).
 (Enter your answer using interval notation.)


(e) Find the range of
f −1(y).
 (Enter your answer using interval notation.)

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10. –/1 points AxlerPreCalc2 1.6.042. My Notes
Question Part
Points
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1
–/1
0/50
Total
–/1
 
Give an example of two increasing functions whose product is not an increasing function. [Hint: There are no such examples where both functions are positive everywhere.]
(f(x), g(x)) = 

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11. –/1 points AxlerPreCalc2 1.R.023. My Notes
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Submissions Used
1
–/1
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–/1
 
Is the product of two odd functions (with the same domain) an even function, an odd function, or neither?
    

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