Lesson 44.5.

NOTE: Be sure to read  Homework Format  and Homework Writing Policy BEFORE writing up your solutions to be turned in.
PROBLEMS WILL NOT BE GRADED AND NO CREDIT WILL BE GIVEN if these guidelines are not followed.

Last modified Apr 14, 2008 8:48 AM

Due Friday, April 18
(If you have done any of these problems correctly before, you can copy and paste or cut and paste your previous solution(s), as long as it is clear what you are doing and the result is easy to check.
Or, attach a cover sheet to your previous homework, noting which problems should be graded here.)

All functions considered below are assumed to have domain and codomain equal to the set of real numbers.
Sect. 7:
  1. Consider the function  f  defined as follows:
        For  x ≤ 0,  f(x) = x;
        For  x > 0,  f(x) = x + 1.
    Determine whether  f  is injective, and prove your answer.

  2. Prove or disprove:
    If the function  f  is increasing on the interval  [0, 1],  then  f([0, 1])  = [ f(0), f(1)].
    Give a clear, complete proof (or disproof), using only simple algebra.

  3. Prove or disprove:
    If the function  f  has a minimum  m1  and a maximum  m2  on the interval  [0, 1],  then  f([0, 1])  = [m1, m2].
    Give a clear, complete proof (or disproof), using only simple algebra.

  4. Prove or disprove:
    If the function  f  has a negative minimum  m  on the interval  [0, 1],  and  f(0) = f(1) = 0,  then  [m, 0]  is a subset of  f([0, 1]).
    If you believe this is true, give a clear, complete proof. If you believe this is false, give a clear, complete counterexample, with explanation and graph. (You don't have to give the proof for the counterexample, but you should be able to prove it is a counterexample by using only simple algebra.)

NOTE: Be sure to read  Homework Format  and Homework Writing Policy BEFORE writing up your solutions to be turned in.
PROBLEMS WILL NOT BE GRADED AND NO CREDIT WILL BE GIVEN if these guidelines are not follows.


NOTE: As stated on the Course Home Page, all due dates are tentative. Assignments, or parts of assignments, may be postponed to a later date.


Last modified Apr 14, 2008 8:48 AM

Go to Lesson 42a (due April 14).

Go to Lesson 46 (due April 14).

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