Can someone point me to a starting point in graphing

f(x)= 25/cos x

If it weren't a fraction and a cosine, I'd try to build a table of coordinates. This one, I have no start point.


To graph the function f(x) = 25/cos(x), you can follow these steps:

1. Determine the domain: Since the function involves a cosine term in the denominator, we need to make sure that cos(x) is not equal to zero. The cosine function is equal to zero at x = π/2, 3π/2, 5π/2, etc. So the domain of f(x) is all real numbers except for these values.

2. Find some key points: To get a sense of the graph, you can start by finding some key points. Plug in a few values of x to evaluate f(x) and generate coordinates. For example:

- Let x = 0: f(0) = 25/cos(0) = 25/1 = 25
- Let x = π/4: f(π/4) = 25/cos(π/4) = 25/√2 ≈ 17.70
- Let x = π/2: f(π/2) = 25/cos(π/2) = 25/0 (undefined)

3. Plot the points: Using the coordinates you found, plot the points on a graph.

4. Observe the behavior: Since cos(x) is a periodic function, the graph of f(x) will also have a periodic pattern. Notice that as cos(x) approaches zero, the value of f(x) becomes very large. However, as cos(x) gets close to ±1, f(x) approaches 25. Use this information to sketch the shape of the graph between your key points.

5. Draw the graph: Connect the plotted points smoothly, following the behavior discussed earlier. Keep in mind the domain restrictions for the function.

Remember, graphing is a visual tool, so it's helpful to have a graphing calculator or software to plot the function accurately.