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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.
 one year ago
 one year ago
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.
 one year ago
 one year ago

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ryoblckBest 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.
 one year ago

Mr.MathBest 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?
 one year ago

ryoblckBest 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.
 one year ago

Mr.MathBest 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.
 one year ago

ryoblckBest 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?
 one year ago

ryoblckBest ResponseYou've already chosen the best response.0
Then how is the outcome still negative?
 one year ago

Mr.MathBest 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?
 one year ago

ryoblckBest 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?
 one year ago
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