Geomenty Assistance

[calvir]

Consider the function f x) - sin(x) where x is in the radians. What types of transformations are being applied to f(x) to produce g(x) - 3 sin(2pi-4pi)) + 10? List thm in the order you would apply them. Be specific.

I came up with the following answers:

1. Vertical stretch by 3
2. Horizontal compression of 2pi
3. Horizontal shift right by 4pi
4. Vertical shift up by 10

What are the amplitude, midline, and the period of g(x)?

I came up with the following answer.

Amplitude = 3
Midline = 10
Period = 2pi over 2pi = 1

My professor has admitted to there being errors but also stated that I did not scale it correctly. I am at a loss and looking for assistance.

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virellt@yahoo.com

Caleb​

 

[Dr.Peterson]

Consider the function f x) - sin(x) where x is in the radians. What types of transformations are being applied to f(x) to produce g(x) - 3 sin(2pi-4pi)) + 10? List thm in the order you would apply them. Be specific.

I came up with the following answers:

1. Vertical stretch by 3
2. Horizontal compression of 2pi
3. Horizontal shift right by 4pi
4. Vertical shift up by 10

What are the amplitude, midline, and the period of g(x)?

I came up with the following answer.

Amplitude = 3
Midline = 10
Period = 2pi over 2pi = 1

My professor has admitted to there being errors but also stated that I did not scale it correctly. I am at a loss and looking for assistance.​

​

Hi, Calvir.

Assuming the equations are really f x) = sin(x) and g(x) = 3 sin(2pi x - 4pi)) + 10, your three answers are correct. But your graph will be wrong, because your horizontal transformations are in the wrong order. In fact, horizontal transformations are done in the opposite order to what everyone expects when he first sees this! When written as f(ax + b), not only does a shrink the graph (if a>1) and b shift left (if b>0), but the shift must be done before the shrink.

Here is an explanation I gave at another site: Order of Transformations of a Function.

There are several ways I have seen textbooks teach this in the case of trig functions; you may want to show us how you were taught to do it, if it doesn't match my suggestion. The form in which your function is written often causes students trouble when they go to graphing the function. For a way that is easier to graph, see Order of Transformations of a Function, Yet Again.

I also recommend checking your graph: Choose a point or two on the graph you drew (e.g. a high point on the sine), put that x into g, and make sure y is what you graphed. This is important as a way to check your thinking, especially when there are two horizontal transformations.