the graph of f(x)=sin (x) is transformed into a new function g(x) by stretching it vertically by a factor of 4 shifting it 3 units to the right. what is the equation of the new function g(x)?

stretch: 4sin(x)

shift: 4sin(x-3)

Thanks Steve! Means a lot!

To find the equation of the new function g(x), we can apply the given transformations to the original function f(x) = sin(x).

Firstly, let's consider the vertical stretching. When a function is stretched vertically by a factor of "a", we multiply the function by that factor. In this case, the function is stretched vertically by a factor of 4.

So, the stretched function is 4*f(x) or 4*sin(x).

Next, let's look at the horizontal shifting. Shifting a function "a" units to the right is achieved by replacing "x" with "(x - a)" in the function. In this case, the function is shifted right by 3 units.

Therefore, the final equation of the new function g(x) is:
g(x) = 4*sin(x - 3)

The function g(x) is the result of vertically stretching the function sin(x) by a factor of 4 and shifting it 3 units to the right.