Question

Which of the following graphs best represents f(x) = 3 sin 4x + 2?

Answer 1

The graph for
f(x) = sin x
is a sinusoidal graph with the origin as the middle point and the value increases up to the maximum point before going down crossing the x-axis and reaching the minimum point before increasing again until it crosses the x-axis. The graph continues as a wave on both sides indefinitely.
f(x) = 3 sin 4x
has an amplitude of 3 or the highest point is 3 and a period of
Period = 2π/4 = π/2
f(x) = 3 sin 4x + 2
the graph is shifted 2 points upward.