The function y = 1/x^2 is defined for all real values of x except for where the denominator equals zero. This brings us to the domain of the function.
Domain: The value of x cannot be zero because division by zero is undefined. Therefore, the domain of the function can be expressed in interval notation as:
- Domain: (-∞, 0) ∪ (0, ∞)
This means that any real number except zero can be used as an input for the function.
Range: Now, let’s consider the range. Since x is squared in the denominator, 1/x^2 will always produce a positive output for any non-zero value of x. As x approaches zero from either the positive or negative side, the value of y approaches infinity. Conversely, as x moves further away from zero (in either direction), the value of y approaches zero but never actually reaches it. Therefore, the range is:
- Range: (0, ∞)
In summary, the function y = 1/x^2 has a domain of (-∞, 0) ∪ (0, ∞) and a range of (0, ∞).