Would you mind helping me please?

Question

The graph of y=sin(x) is vertically stretched by a factor of 15, shifted a distance of 6 units to the right, and translated 8 units upward.Find a formula for the function whose graph is the resulting graph.

Answer 1

Thanks for adding the missing info! :)

To show a vertical stretch, we attach the factor to the front of the function:

y = 15 * sin(x)

When shifting left or right, the shift is shown in the parentheses with the x (since we are moving the graph along the x-axis). If it is shifted to the left, the number will be added. If it is shifted to the right, we subtract it. For this example we are shifting to the right so we will subtract the unit:

y = 15 * sin(x - 6)

Finally, when we shift up or down, the shift is shown outside of the parentheses. If we shift up, we add the shift and if we move down we subtract. In this case we are moving up 8 units so we will add 8:

y = 15 * sin(x-6) + 8

I hope this explanation was thorough and answered all of your questions. If you have additional questions please don't hesitate to reach out! Learn on :)