The graph of f(x)=cos(x) is transformed to a new function, g(x) , by stretching it horizontally by a factor of 4 and shifting it 1 unit up.

What is the equation of the new function g(x)?

g(x)= ?

The equation of the new function is

Explanation:

The Parent function is

We need to determine the new function g(x) using the transformation by stretching the f(x) horizontally by a factor of 4 and shifting it 1 unit up.

The function transformation formula is given by

Where a stretches the function vertically

b compresses or stretches it horizontally,

c shifts the function left or right

d shifts the function up or down

Since, it is given that the function stretches horizontally by a factor of 4 and shifting it 1 unit up.

Hence, and

Substituting these values in the formula, we have,

Thus, the equation of the new function is

c

step-by-step explanation: