Do all exponential functions go through the point (0, 1)?
If so, why is this the case?
The math book does not share the "WHY" with its readers.
I am just curious.
The equation of the function could be: . A point of the graph of this function has the coordinates P(x, y) or in words:
P is on the graph if the coordinates consist of (exponent, value of the power). The base is considered to be a constant.
If the exponent is zero, the value of the power is which is by definition 1.
And therefore the graphs of all exponential functions with the equation mentioned above will pass through the point P(1, 0)
All she said was this:
It depends on how you define the exponential function.
If we have an exponential function where has a constant value, the value of the function at x=0 is , thus it passes through the point .
However, if you defind an exponential function as , where b is some number, then the value of the function at x=0 is , thus it passes through the point
This shouldn't be that hard to grasp.