Question

Using g(x)=-2.5sin(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)?

Answer 1

I don’t see the x-values or the candidate graphs in your question. Could you post the table of x-values (the “first row”) and the picture/labels of the graph choices?

Meanwhile, here is how to do it and an example for a common set of x-values:

Method
- Make sure your calculator is in radian mode (x+1.5 is in radians).
- For each x, compute y = -2.5·sin(x + 1.5).
- Round as needed.

Example (for x = -3, -2, -1, 0, 1, 2, 3)
- x = -3: y = -2.5·sin(-1.5) ≈ 2.494
- x = -2: y = -2.5·sin(-0.5) ≈ 1.199
- x = -1: y = -2.5·sin(0.5) ≈ -1.199
- x = 0: y = -2.5·sin(1.5) ≈ -2.494
- x = 1: y = -2.5·sin(2.5) ≈ -1.496
- x = 2: y = -2.5·sin(3.5) ≈ 0.877
- x = 3: y = -2.5·sin(4.5) ≈ 2.444

Graph features to identify g(x)
- Amplitude 2.5 (y-values range between -2.5 and 2.5).
- Reflected vertically (leading negative) so it starts as a descending sine wave relative to the usual sin shape.
- Phase shift left by 1.5 units (because of x + 1.5).
- Period 2π.

If you paste the x-values or the images/labels of the graph choices I’ll compute the exact y-values and pick which graph matches.