For the given graph of y=f(x), sketch the graph y=1/f(x). clearly show the asymptote(s) with a dotted line and write the coordinates of the invariant points
well, the vertical asymptotes will be where f(x) = 0
invariants are where f(x) = x
Other than that, I can't help you without more information on f(x)
To sketch the graph of y=1/f(x) using the given graph of y=f(x), follow these steps:
1. Start with the graph of y=f(x).
2. Identify the points where the graph of f(x) intersects the x-axis. These are the points where f(x) = 0. Let's call these points (a, 0). Note the x-coordinate of each zero point.
3. Plot these zero points on the x-axis of the new graph.
4. Determine the y-values for each of these zero points on the y=1/f(x) graph. Since 1/0 is undefined, we will have vertical asymptotes at these points. Let's label these asymptotes as vertical dotted lines.
5. Now, consider the y-values of the points on the original graph. For each y-value y1, calculate the reciprocal (1/y1). Plot these new points on the y=1/f(x) graph, with their corresponding x-coordinate.
6. Connect the points on the y=1/f(x) graph, keeping in mind the vertical asymptotes.
Remember to clearly label the asymptotes with dotted lines and write down the coordinates of any invariant points (unchanged points).
By following these steps, you will be able to sketch the graph of y=1/f(x) using the given graph of y=f(x).