Question

How many times does the graph of y=0.1x intersect the graph of y=sin(2x)?

Answer 1

the line y=0.1x is in the range of the sin function from -10 to 10
0.1*-10 = -1
0.1*10 = 1
period of sin(2x) is pi
10/pi = 3.18
so approximately 3 cycles on either side of origin intersecting 2 times per cycle
Also at x=0, it double counts so take away 1
6*2 -1 = 12-1 = 11
They intersect 11 times
verify by graphing