Science:Math Exam Resources/Courses/MATH104/December 2011/Question 01 (k)
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q1 (g) • Q1 (h) • Q1 (i) • Q1 (j) • Q1 (k) • Q1 (l) • Q1 (m) • Q1 (n) • Q2 (a) • Q2 (b) • Q2 (c) • Q2 (d) • Q2 (e) • Q2 (f) • Q2 (g) • Q3 • Q4 • Q5 (a) • Q5 (b) • Q5 (c) • Q5 (d) • Q6 (a) • Q6 (b) • Q6 (c) • Q6 (d) • Q6 (e) •
Question 01 (k) 

Let g be a continuous function on a close interval [0,1]. Let g(0) = 1 and g(1) = 0. Which of the following is NOT necessarily true?

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Try to think back to the theorems and definitions in this course and see which statements are satisfied by these theorems and definitions. 
Hint 2 

The following theorems and definitions might be useful: The intermediate value theorem, The extreme value theorem, The definition of continuity. 
Hint 3 

Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. The correct answer is (d). Let's examine each possibility. (a) Since is continuous, we can use the extreme value theorem which says exactly what (a) is telling us  there is a maximum value on the interval (b) This is saying that if two values are equal then their function values are equal. Since a function can only take one output value for each input value, this is a true statement. (c) Since and is continuous, then the intermediate value theorem tells us exactly what this statement says, there is a value c in such that (d) This statement is false. The difference between (c) and this problem is that the number 3/2 does not lie between and . A counter example would be a straight line joining and . This can be described by . (e) This is true as this is the definition of continuity and is given to be continuous. 