f (x)=square root of 9-x^2
show me the steps
Thank You :)
show me the steps
Thank You :)
-
Domain: [-3,3]
Range:[0,3]
okay first for domain, which is all possible values of x. Now in this equation it would be [-3,3] because we cannot take the square root of a neg number, and the only way we can take a root of a +/0 number is if x is between -3 and 3 inclusive.
For the range, or y, just remember what we said above, the lowest value to take the root of in this case is a 0, so 0 is your lowest possible y. For the highest again, it would mean that x=0 and you subtract nothing from 9 ( cause you can't change the -x^2 to a +x^2 cause x^2 must be positive and - x + = - ). So highest would be 3
Range:[0,3]
okay first for domain, which is all possible values of x. Now in this equation it would be [-3,3] because we cannot take the square root of a neg number, and the only way we can take a root of a +/0 number is if x is between -3 and 3 inclusive.
For the range, or y, just remember what we said above, the lowest value to take the root of in this case is a 0, so 0 is your lowest possible y. For the highest again, it would mean that x=0 and you subtract nothing from 9 ( cause you can't change the -x^2 to a +x^2 cause x^2 must be positive and - x + = - ). So highest would be 3
-
Basically, the domain is the x values...the range is the y values
Do you have a graphing calculator? If not, you can find ones online. If so, you should graph it.
To find domain, you look at which x values can make this function real (not negative number inside square root, etc.). So, you set 9 - x^2 = 0
x^2=9
x=3
So, if x equaled 3, then the you would get sqrt( 0 ), which would be zero. You cannot make x above nor below 3 since that would make sqrt( negative number)
So the domain is from -3 to 3
The range is y values. You know that you cannot have y < 0 because square roots are always positive. Also, you know you cannot have y > 3 because the least x can be is 0 (since it's squared) and that would be sqrt (9) which is 3. The range is from 0 to 3.
Hope this helped, if any questions or still confused, just add details
Do you have a graphing calculator? If not, you can find ones online. If so, you should graph it.
To find domain, you look at which x values can make this function real (not negative number inside square root, etc.). So, you set 9 - x^2 = 0
x^2=9
x=3
So, if x equaled 3, then the you would get sqrt( 0 ), which would be zero. You cannot make x above nor below 3 since that would make sqrt( negative number)
So the domain is from -3 to 3
The range is y values. You know that you cannot have y < 0 because square roots are always positive. Also, you know you cannot have y > 3 because the least x can be is 0 (since it's squared) and that would be sqrt (9) which is 3. The range is from 0 to 3.
Hope this helped, if any questions or still confused, just add details