Answer: f(x) = 0.5*sec(x)
===========================================================
Step-by-step explanation:
The graphs for secant and cosecant are disconnected sets of "parabolic" curves. I put it in quotes because those aren't really parabolas even if they might look it.
If we plugged x = 0 into y = csc(x), then you'll find that y = undefined. This is due to a division by zero error.
- csc(x) = 1/sin(x)
- If x = 0, then sin(x) = 0 and csc(x) = 1/0 = undefined
This basically rules out csc(x) because the given graph clearly shows x = 0 is in the domain.
Luckily sec(x) works when x = 0. It leads to y = 1
- sec(x) = 1/cos(x)
- If x = 0, then cos(x) = 1 and sec(x) = 1/1 = 1
In other words, the point (0,1) is on the curve y = sec(x).
If the function was f(x) = 0.5sec(x) then f(0) = 0.5 to match the graph.
I recommend using either GeoGebra or Desmos as a graphing tool. Both can handle the trig functions mentioned. Make sure you adjust the x-axis scale to include things like pi/2, pi, 3pi/2, etc.