State the domain and range of each function. Justify your answer.  y= 2(x-3)^2 + 1

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Hi, super,

The domain of this function is "all real numbers".  Many times, but not everytime, you would simply consider "the nature of the function".  As in, with this function, you can plug in anything for x and get something out.  It's not like y = 1/x, where x can't...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

Hi, super,

The domain of this function is "all real numbers".  Many times, but not everytime, you would simply consider "the nature of the function".  As in, with this function, you can plug in anything for x and get something out.  It's not like y = 1/x, where x can't be 0, because you would divide by 0.  Here, you don't have to worry anything about that.  The domain is "all real numbers".

For the range, though, you can assume that the squared part has to be greater than or equal to 0.  That part, (x-3)^2, can't be negative.  So, we would have:

(x-3)^2 >= 0

Then, to make it like the function we have, we can multiply each side by 2:

2(x-3)^2 >= 0

Then, add 1 to each side

2(x-3)^2 + 1  >= 1

The left side is y.  So:

y >= 1.

And, y represents the range.  So, for this function, the range has to be greater than or equal to 1.

Good luck, super.  I hope this helps.

Till Then,

Steve

Approved by eNotes Editorial Team