The functionf(x) is multiplied by a factor of 2 and then 3 is added to the function.



f(x)=sin(x)

What effect does this have on the graph of the function?



The graph is vertically compressed by a factor of 3 and shifted up 2 units.

The graph is vertically stretched by a factor of 2 and shifted up 3 units. <my choice

The graph is vertically compressed by a factor of 2 and shifted up 3 units.

The graph is vertically stretched by a factor of 3 and shifted up 2 units.

To determine the effect of multiplying the function f(x) by 2 and then adding 3 to the function, you need to analyze each transformation separately and then combine them.

First, let's consider the effect of multiplying the function f(x) by 2. When you multiply a function by a positive constant, it results in a vertical stretching or compression of the graph. If the constant is greater than 1, the graph is vertically stretched, and if the constant is between 0 and 1, the graph is vertically compressed.

In this case, since the constant is 2 (which is greater than 1), the graph of f(x) = sin(x) will be vertically stretched by a factor of 2.

Now, let's consider the effect of adding 3 to the function. When you add a constant to a function, it results in a vertical shift of the graph. If the constant is positive, the graph is shifted upward, and if the constant is negative, the graph is shifted downward.

In this case, since the constant is 3 (which is positive), the graph of f(x) = sin(x) will be shifted upward by 3 units.

Finally, we need to combine the two transformations. Since the vertical stretching occurs first in the sequence of transformations, the graph will be vertically stretched by a factor of 2. Then, the vertical shift will be applied, shifting the graph upward by 3 units.

Therefore, the correct answer is:

The graph is vertically stretched by a factor of 2 and shifted up 3 units.

The correct answer is: The graph is vertically stretched by a factor of 2 and shifted up 3 units.

I agree.