Question

Using g(x)=-2.5 sin(x+1.5), find the y-values in the second row by substituting each x-value into the function. Which of the following is the graph of g(x)?
x=0, x=pi/2, x=pi, x=3pi/2

Answer 1

Compute y = -2.5 sin(x + 1.5) at each x:

- x = 0: y = -2.5 sin(1.5) ≈ -2.5(0.997495) ≈ -2.494
- x = π/2: y = -2.5 sin(π/2 + 1.5) ≈ -2.5(0.070737) ≈ -0.177
- x = π: y = -2.5 sin(π + 1.5) ≈ -2.5(−0.997495) ≈ +2.494
- x = 3π/2: y = -2.5 sin(3π/2 + 1.5) ≈ -2.5(−0.070737) ≈ +0.177

So the points are approximately:
(0, −2.494), (π/2, −0.177), (π, 2.494), (3π/2, 0.177).

The correct graph is the sine wave with amplitude 2.5, vertically flipped, shifted left by 1.5 radians, and passing through those points (minimum near x = 0, maximum near x = π). Pick the option that matches that behavior.