"The base of y = sin x has been transformed. It now has an amplitude of 8.6, a period of 28, a phase shift of 10 units to the right, a vertical translation of 2.5 units down, and a reflection to the x-axis. Given that (π/6, 1/2), is a point in the base function, use mapping notation to determine the x-coordinate of it's image point in the transformed function.

Question

"The base of y = sin x has been transformed. It now has an amplitude of 8.6, a period of 28, a phase shift of 10 units to the right, a vertical translation of 2.5 units down, and a reflection to the x-axis. Given that (π/6, 1/2), is a point in the base function, use mapping notation to determine the x-coordinate of it's image point in the transformed function.

Enter numerical value of the x-coordinate only and rounded to two decimal places"

I have an idea on how to do this question, but I just really need some quick confirmation: the reflection of the x-axis will NOT AFFECT the X-INTERCEPT, only the y-intercept, right?

Answer 1

Correction: the reflection of the x-axis will NOT AFFECT the X-COORDINATE, only the y-coordinate, right?

Answer 2

that is correct.

Answer 3

Yes, that's correct. The reflection of the x-axis will only affect the y-values or the vertical translations of the function, not the x-values or the horizontal translations. Therefore, the x-intercepts or the points where the function crosses the x-axis will not be affected by the reflection.