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

g (x) = 4 sin (x - 3)

Step-by-step explanation:

The given function is:

f (x) = sin (x)

Stretching by a factor of 4:

A vertical stretch or compression of f (x) can be expressed as:

cf (x), where c is any constant

if c > 1, it indicates a stretch in vertical direction and if 0 < c < 1, it indicates a compression by a factor of c in vertical direction.

Since, given function is being stretched by a factor of 4, the transformed function will become:

4f (x)

Shifting by 3 units right:

A shift of f (x) to right can be obtained by subtracting c from every occurrence of x in f (x), where c is the number of units f (x) is being shifted in right direction. Since in this case f (x) is shifted 3 units to right, the transformed function will be:

f (x - 3)

Applying both the transformations to f (x), we get g (x) as:

g (x) = 4 f (x - 3)

g (x) = 4 sin (x - 3)