y=12^x
What does this mean and how do you explain it on a graph?
The equation y=12^x represents an exponential function. In this case, the base of the exponential function is 12, and the variable x represents the exponent.
To explain it on a graph, you can follow these steps:
1. Choose some values for x. For simplicity, let's say x can take on the values -2, -1, 0, 1, and 2. These values will help us plot points on the graph.
2. Substitute these values of x into the equation to find the corresponding values of y. For example, when x=-2, y=12^(-2)=1/144. Similarly, when x=-1, y=12^(-1)=1/12. When x=0, y=12^0=1. When x=1, y=12^1=12. Lastly, when x=2, y=12^2=144.
3. Plot the points (x, y) on a coordinate axis. The points we found earlier are (-2, 1/144), (-1, 1/12), (0, 1), (1, 12), and (2, 144).
4. Connect the points with a smooth curve. Since it is an exponential function, the curve will be steep and gradually increase or decrease, depending on the sign of the exponent.
5. Label the axes as "x" and "y" to indicate the variables being represented. Include any necessary units or scaling labels.
The resulting graph will show a curve that slowly increases or decreases depending on the sign of x. The base 12 ensures that the graph is steeper compared to exponential functions with smaller bases.