What is the range of the function \(y = x^2\)?

What is the range of the function \(y = x^2\)?

• A. [0, 1]
• B. [0, \infty)
• C. [-\infty, \infty]
• D. [1, \infty)

Answer: (B)

To determine the range of the function \(y = x^2\), it is essential to understand the behavior of the function as \(x\) varies over all real numbers. The function \(y = x^2\) is a quadratic function that opens upwards, forming a parabola. As \(x\) takes on any real number value, \(y\) calculates the square of that value. The output of squaring any real number is always non-negative because the square of a positive number is positive and the square of zero is zero. Moreover, for any negative value of \(x\), squaring it will also yield a non-negative result, as the product of two negative numbers is positive. Thus, the minimum value of \(y\) occurs when \(x = 0\), yielding \(y = 0\). As \(x\) moves away from zero in either direction (positive or negative), \(y\) increases without bound. Therefore, the possible outputs (or range) of the function start from 0 and extend infinitely upwards. This behavior leads to the conclusion that the range of \(y = x^2\) is all values from 0 to infinity, inclusive of 0. This is

To determine the range of the function (y = x^2), it is essential to understand the behavior of the function as (x) varies over all real numbers. The function (y = x^2) is a quadratic function that opens upwards, forming a parabola.

As (x) takes on any real number value, (y) calculates the square of that value. The output of squaring any real number is always non-negative because the square of a positive number is positive and the square of zero is zero. Moreover, for any negative value of (x), squaring it will also yield a non-negative result, as the product of two negative numbers is positive.

Thus, the minimum value of (y) occurs when (x = 0), yielding (y = 0). As (x) moves away from zero in either direction (positive or negative), (y) increases without bound. Therefore, the possible outputs (or range) of the function start from 0 and extend infinitely upwards.

This behavior leads to the conclusion that the range of (y = x^2) is all values from 0 to infinity, inclusive of 0. This is