Which of the following equation represents a function?

Concept:

Function: An equation is said to be a function if, for each possible input value, there is exactly one output value.

Explanation:

Here the equation can be f(x) or f(y), so the equation which will satisfy the above criteria can be called a function.

Equation 1) |x| + |y| = 2

• This equation cannot be a function of x or y since modulus will always give two values for x or y.

Equation 2) |x + y| = 2

• This equation cannot be a function since opening the modulus bracket gives two values to both x and y.

Equation 3) |y| = x2 + sin x

• This equation cannot be a function since due to |y| the negative part of RHS will reflect from the Y-axis and finally, it will give multiple y for the same x

Equation 4) |x|2 - x

• Assuming the equation as y = |x|2 - x, it becomes a function of x.
• For every x, there is only one value of y.

Hence, the required equation which can be called a function is |x|2 - x.