What are the domain, range, roots, and asymptotes of…

label Calculus
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What are the domain, range, roots, and asymptotes of…

a) f(x)= √(a^2-x^2)

b) f(x)= ⟦x⟧

Aug 24th, 2015

Hi there! Thank you for the opportunity to help you with your question!

The domain of sqrt(a^2-x^2) is whenever the argument is greater than or equal to zero which means:

a^2 - x^2 >=0 

a^2 >= x^2

-a<=x<=a

The range is from 0 to a, or [0,a] including both endpoints

The roots are x= a and x = -a

There are no asymptotes

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The domain of the greatest integer function is all real numbers (-infinity, infinity)

The range is every integer (x in Z)

The roots are actually a range of number from [0,1)

There are no asymptotes



Please let me know if you need any clarification. Always glad to help!
Aug 24th, 2015

Also, how would the graph of f(x)= √(a^2-x^2)  look like?

Aug 24th, 2015

That graph is actually a semicircle with radius a, in the upper plane. Some points in the graph include (-a, 0),"(0,a), (a, 0)

Aug 25th, 2015

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