Finding Domain and Range

flamathdummy said:
y = x^2 + 4x + 1
Domain is easy, for this one. What values for x do NOT work in the expression? Domain is ALL Real Numbers.

Range is a matter of experience. What values can you get out of it? If you recognize the structure, it's a parabola with a positive leading coefficient. This implies that it opens UP or has a minimum value. Completing the square will help you find it.

(x^2 + 4x + 4) + 1 - 4 = (x+2)^2 - 3

The minimum is -3, so [-3,big] is the Range.
 
tkhunny said:
flamathdummy said:
y = x^2 + 4x + 1
Domain is easy, for this one. What values for x do NOT work in the expression? Domain is ALL Real Numbers.

Range is a matter of experience. What values can you get out of it? If you recognize the structure, it's a parabola with a positive leading coefficient. This implies that it opens UP or has a minimum value. Completing the square will help you find it.

(x^2 + 4x + 4) + 1 - 4 = (x+2)^2 - 3

The minimum is -3, so [-3,big] is the Range.
So after I complete the square

(x + 2)^ -3 = (x + 2)^2 - 3....this gives me the -3, +infinity...right???
 
flamathdummy said:
-3, +infinity...right???
Right. Sorry about that. That's what "big" is in my mind. Too much confusion about what "infinity" means or is.
 
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