I'm a little confused here. I have a function: f(x) = x^2 + 3(adsbygoogle = window.adsbygoogle || []).push({});

If the domain of the function is

-3 <= x <= 3

I need to find the range...

I think that the answer is 3 <= y <= 12... that can be found out by drawing the graph. But I want to find the range algebraically. It says in my text book to turn the 'x' in the middle of the domain shown above into the respective f(x) equation (x^2)+3... and performing whatever action on x on the other sides of the inequality. This works in other functions, but I think I'm doing something wrong with this one:

1.-3 <= x <= 3

2.9 <= x^2 <= 9

3.12 <= x^2 + 3 <= 12

I think that because in step 1 I multiplied one value by (-3) I need to flip the greater than/equal to sign(s), but not sure how to do it... as you can see, by step 3, the wrong answer is reached. Can anyone show me my mistake? Thanks!

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# Homework Help: Domain / range of a function

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