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What is the domain and range of # f(x) = 2x^2 - 3#?

Answer 1

graph{2x^2-3 [-10.07, 9.93, -3.86, 6.14]} So this shown above #uarr# is the graph for #f(x)=2x^2-3#.
Domain: #x=oo#
Range: #y > -3#

The definition of domain is the set of #x# values on the graph. The definition of the range is the set of #y# values on a graph. So when you look at the domain you look at the #x#-axis (horizontal line). So where does the line stop and start on the #x#-axis? it goes on forever right? Because the side keeps expanding forever and ever so the domain would equal #oo# ... Now let's look at the range. The range is the set of y-values so if you have a paper on this tilt it so it's easier to see it looks like a big arrow, <. So the tip of this "arrow" touches -3 and then goes on forever and ever... so you can either put y>-3 (y is bigger than negative 3) or, #-3 < y < oo # (-3 is smaller than y but goes on forever). Hope this was understandable please comment below if you have concerns...

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Answer 2

Eva Abramson

The domain of the function f(x) = 2x^2 - 3 is all real numbers, and the range is all real numbers greater than or equal to -3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.