For the following exercises, use a graphing calculator to graph two periods of the given function. Note: most graphing calculators do not have a cosecant button; therefore, you will need to input csc x as 1/sin x.

The function f(x) = 20tan (π/10 x) marks the distance in the movement of a light beam from a police car across a wall for time x, in seconds, and distance f(x), in feet.

a. Graph on the interval [0,5].

b. Find and interpret the stretching factor, period, and asymptote.

c. Evaluate f(1) and f(2.5) and discuss the function’s values at those inputs.