The graph of the function y = sin(x) is translated units to the left, and then each point's abscissa on the graph is changed to (ω > 0) times the original (the ordinate remains unchanged) to obtain the graph of the function y = f(x). If the function y = f(x) has only one zero in the interval (0, ), find the range of ω.
Pick one
Solution
After translating the graph of y = sin(x) units to the left, we get the graph of y = sin().
Then, changing each point's abscissa to times the original, we obtain the graph of f(x) = sin().
In the interval (0, ), .
If the function y = f(x) has only one zero in the interval (0, ), then , hence ω ∈ .
Thus, the answer is: .
This solution uses the properties of the graph transformation rules for the function y = Asin() and the zeroes of the sine function. The problem primarily assesses understanding of the graph transformation rules for functions of the form y = Asin() and the zeroes of the sine function, making it a fundamental question.
Want a route through all this instead of an archive? The track
puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.