how do you determine the inverse of a function with a chart?????
It depend on what function, and what chart you are using.
which line is steeper y=5/3X-2 or y=3/2X+3?
To determine the inverse of a function using a chart, you need to follow these steps:
1. Begin with a chart that shows the function's input and output values. Let's say the function is denoted as f(x).
2. Swap the input and output values in the chart. This means you will interchange the x-values (inputs) with the corresponding f(x)-values (outputs).
3. Identify any repeating elements in the swapped chart. If there are duplicate x-values in the swapped chart, the function does not have an inverse, as it fails the horizontal line test. In this case, multiple y-values correspond to the same x-value, making it impossible for us to obtain a unique inverse.
4. If there are no repeating elements, label the swapped x-values as y and the swapped f(x)-values as x. Now you have a new chart with the inverse function.
5. Finally, express the inverse function using the new x and y values. Replace the y with f^(-1)(x) (read as "f inverse of x"). The inverse function is thus represented as f^(-1)(x) = y.
Note that the chart-based method works best when the given function has a limited set of inputs and outputs. If the function is represented by an equation, using algebraic methods might be more efficient to find the inverse.