The modulus function, denoted as |x|, is a mathematical function that returns the absolute value of a number. It essentially gives the distance of a point from the origin on a number line.
The modulus function is used in this equation to ensure that the result is always positive. This is because the square root of a negative number does not have a real solution, so the modulus function is used to eliminate any negative values of x.
Yes, the equation can have two solutions - one for positive x values and one for negative x values. For example, if x = 3, the equation becomes Sqrt(3^2) = |3|, which simplifies to Sqrt(9) = 3, and if x = -3, the equation becomes Sqrt((-3)^2) = |-3|, which also simplifies to Sqrt(9) = 3.
Since the modulus function returns positive values, the graph of "Sqrt(x^2) = |x|" will only be in the positive x-axis. It will start at the origin, extend to the right, and then curve upwards. The graph will be a V-shaped graph with the vertex at the origin.
The domain, or input values, of the equation is all real numbers. The range, or output values, is also all real numbers, but only positive values since the modulus function always returns positive values.