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Domain and Range

Let's look at another one:

Let's find the domain and range of this guy:

y = -( x )^2 + 3

Hmm...  Well, I can't THINK of any x's that can't be put into this thing...  But, what about the range?

We really need to graph it.

y = -( x )^2 + 3 ... the -( x )^2 part means that it's an upside down standard parabola ... the + 3 means that the graph is shifted up three a graph of an upside down standard parabola shifted up three ... the y guys go from 3 down

Again, the domain will be all x's (since he spreads out forever).  And the range goes from 3 down...

domain = ( -infinity , infinity )
range = ( -infinity, 3 ]

 

TRY IT:

From the graph of y = x^2 - 4 , find the
domain and range.