The range of the function y = x² is the set of all possible output values (y-values) that the function can produce. To determine the range, we start by recognizing that this function is a quadratic function, and its graph is a parabola that opens upwards.
In the case of y = x², regardless of the value of x (which can be any real number), squaring x will always yield a non-negative result. This means that:
- If x is positive, x² is positive.
- If x is zero, x² is zero.
- If x is negative, squaring x will still yield a positive result (since multiplying two negative numbers yields a positive outcome).
Thus, the function produces values starting from zero and increasing infinitely, making the range:
Range: [0, ∞)
In interval notation, this is represented as [0, ∞), which indicates that the function can take any value from 0 to infinity, including 0 itself but not infinity.
Therefore, the concise answer to the question is:
The range of the function y = x² is [0, ∞).