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

a) f(x)= √(a^2-x^2)

b) f(x)= ⟦x⟧

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

--------------------------------------------------------

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)

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

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)

Secure Information

Content will be erased after question is completed.

Enter the email address associated with your account, and we will email you a link to reset your password.

Forgot your password?

Sign Up