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

Answer 1

Genesis Allen

Domain: #{x|x !=0}# or #(-oo, 0)uu(0,oo)#

Range: #{y|y>0}# or #(0, oo)#

#y = 3/x^2#

If the denominator is zero, the function is undefined, so we set it to zero and solve:

#x^2=0#

#x=+-sqrt0#

#x=0#

Thus, the domain is:

#{x|x !=0}# or #(-oo, 0)uu(0,oo)#

Now as #x# gets close to #-oo# or #oo# the function gets closer to 0 but never actually gets to 0 and as #x# gets very close to 0 the function grows to #oo# so the range is:

#{y|y>0}# or #(0, oo)#

graph{x^2 [-10, 10, -5, 5]} = y

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Answer 2

Ethan Adkins

The domain of (y = \frac{3}{x^2}) is all real numbers except (x = 0), represented as ((-∞, 0) ∪ (0, ∞)), because division by zero is undefined.

The range of (y = \frac{3}{x^2}) is (y > 0) because the numerator is a positive constant (3), and the denominator ((x^2)) is always non-negative, resulting in a positive value for (y).

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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.