Is y = 2x + 1 a Function?

Yes, y = 2x + 1 is a function. In mathematics, a function is defined as a relation where each input (or x value) has exactly one output (or y value).

To determine if this equation is a function, we can look at the equation in the form of y = mx + b, where m is the slope and b is the y-intercept. In this case, m is 2, and b is 1. The equation describes a straight line, and every unique input value of x will produce a single unique output value of y.

For example:

  • If x = 0, then y = 2(0) + 1 = 1
  • If x = 1, then y = 2(1) + 1 = 3
  • If x = -1, then y = 2(-1) + 1 = -1

As we can see, each x value corresponds to only one y value, fulfilling the definition of a function. Therefore, the equation y = 2x + 1 is indeed a function.

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