How do you find the domain and range for #y=x^2+3#?

1 Answer
Rhys
Oct 30, 2017

Domain; #x in RR#
Range; #y>=3#

Explanation:

The domain for this function can be considered by considering what values of x make y be defined, and we see evidently that #x# can take on any real value as a simply porabola, with no asymptotes, and y would be defined; so hence #x in RR#

The range can be found by considering the graph of this equation, just #y=x^2# shifted 3 units upward;

graph{x^2+3 [-18.67, 21.33, -1.08, 18.92]}

So from this we see that #y# has the smallest value at 3, where # x=0# and otherwise is #>3#

hence # y# is always 3 or greater.

Hence yielding a range of; #y>=3#

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