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ryoblck
Group Title
7. Which if the following is always true of odd functions?
I. f (−x) = −f(x)
II. f(x) is even
III. f(x) is even
A. All of these are true.
B. None of these are true.
C. I only.
D. II only.
E. I and III only.
 2 years ago
 2 years ago
ryoblck Group Title
7. Which if the following is always true of odd functions? I. f (−x) = −f(x) II. f(x) is even III. f(x) is even A. All of these are true. B. None of these are true. C. I only. D. II only. E. I and III only.
 2 years ago
 2 years ago

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Mr.Math Group TitleBest ResponseYou've already chosen the best response.1
What do you think?
 2 years ago

ryoblck Group TitleBest ResponseYou've already chosen the best response.0
I think all of them are true but not too sure. I get confused a lot with these odd and even function questions.
 2 years ago

Mr.Math Group TitleBest ResponseYou've already chosen the best response.1
I will help you out. The definition of an odd function only tells us that a function \(f(x)\) is odd if it satisfies the property: \(f(x)=f(x)\), for all x in the domain of \(f\). Now we know that "I" is true, and we should use to make a conclusion about the other two statements. Would you like to try?
 2 years ago

ryoblck Group TitleBest ResponseYou've already chosen the best response.0
Well wouldn't it still be positive because of the absolute values? And if it is not negative then it is not an odd function.
 2 years ago

Mr.Math Group TitleBest ResponseYou've already chosen the best response.1
In II, we will only have \(f(x)=f(x)=f(x)\), and we can't say it's even. However in III, we have \(f(x)=f(x)=f(x)\), and therefore it's even.
 2 years ago

ryoblck Group TitleBest ResponseYou've already chosen the best response.0
Wait why is that? Because once we put the negative within the absolute values in "II", it should turn positive right?
 2 years ago

Mr.Math Group TitleBest ResponseYou've already chosen the best response.1
Yes; \(x=x\).
 2 years ago

ryoblck Group TitleBest ResponseYou've already chosen the best response.0
Then how is the outcome still negative?
 2 years ago

Mr.Math Group TitleBest ResponseYou've already chosen the best response.1
It can be. Suppose you have \(f(x)=x^3\). Then \(f(x)=(x)^3=x^3\). Right?
 2 years ago

ryoblck Group TitleBest ResponseYou've already chosen the best response.0
Oh so it doesn't matter if the absolute value only covers x? It can still be negative. But if the absolute value covers the whole function, then it will be positive? Correct?
 2 years ago
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