Question

Consider the function f(x) = 2sin(x) - 2. What are the coordinates of the point where the graph intersects the x-axis?

A) (π/2, 0)
B) (π, 0)
C) (3π/2, 0)
D) (2π, 0)

Answer 1

The coordinates of the points where the graph intersects the x-axis are (π/2, 0), (5π/2, 0), etc.

Step-by-step explanation:

The function f(x) = 2sin(x) - 2 represents a sinusoidal function shifted downwards by 2 units. To find the coordinates of the point where the graph intersects the x-axis, you need to set f(x) equal to zero and solve for x.

2sin(x) - 2 = 0

2sin(x) = 2

sin(x) = 1

The sine function equals 1 at the angles π/2, 5π/2, and so on. Since the function is periodic, you can add any multiple of 2π to get other intersecting points.

Therefore, the coordinates of the point where the graph intersects the x-axis are (π/2, 0), (5π/2, 0), etc.