What is the domain and range of #y=x^2 - 4x + 1#?

Answer 1

Hazel Anglin

Range: #y>=-3#
Domain: #x in RR#

When the square is finished, put the function in vertex form.

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

Hence the minimum of the function is #y=-3#, so we can say that the range is

#y>=-3#

As for the domain, any value of #x# can be passed to the function so we say that the domain is

#x in RR#

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Answer 2

Jameson Allen

Domain: All real numbers. Range: The minimum value of the quadratic function occurs at its vertex. To find the vertex, use the formula for the x-coordinate of the vertex: x = -b/(2a), where a = 1, b = -4. Plug in these values to find the x-coordinate of the vertex. Once you have the x-coordinate, substitute it into the quadratic function to find the corresponding y-coordinate. The range will be from this y-coordinate to positive infinity.

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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.