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When graphing functions, the coordinate plane plays a foundational role. It consists of two axes: the horizontal axis (usually labeled as the x-axis) and the vertical axis (labeled as the y-axis). These axes intersect at a point called the origin, denoted as (0,0).

Every point on the plane can be represented by an ordered pair (x, y), where 'x' denotes the position along the horizontal axis and 'y' signifies the position along the vertical axis. In the context of exponential functions like \(y = 60^x\), graphing involves plotting points that represent the function's output for different input values along the x-axis and connecting these points to visualize the growth rate of the function.

Exponential functions frequently require applying the laws of exponents to simplify and evaluate expressions. One of the foundational laws is that any nonzero number raised to the power of 0 equals 1, symbolically expressed as \(a^0 = 1\) provided that \(a eq 0\).

This rule is crucial when dealing with functions like \(y = 60^x\), especially at the point where \(x = 0\). Remembering this law allows for quick evaluation of the function at any point where the exponent is 0, significantly simplifying the function evaluation process.

Function evaluation is the process of finding the output of a function for a specific input. In the case of \(y = 60^x\), the function is defined for all real numbers 'x' and involves raising the base (60) to the power of 'x'.

To determine if a point lies on the graph of an exponential function, we substitute the x-coordinate into the equation and see if the resulting y-value matches the y-coordinate of the point in question. For the point (0,1), substituting 0 for x in accordance with the laws of exponents yields \(60^0 = 1\). The output matches the y-coordinate of the point, confirming that the point indeed lies on the graph of the function.