.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) ?

To find the equation of the new function, g(x), which is obtained by stretching the graph of f(x) = cos(x) horizontally by a factor of 4 and shifting it 1 unit up, we need to apply the appropriate transformations to the original function.

Let's start by looking at the transformations one by one:

1. Stretching horizontally by a factor of 4:
To stretch the graph horizontally by a factor of 4, we need to multiply the x-values by 1/4. This stretches the graph in the x-direction, making it narrower.

2. Shifting the graph 1 unit up:
To shift the graph 1 unit up, we need to add 1 to the y-values. This moves the entire graph vertically upward by 1 unit.

Now, let's apply these transformations to the function f(x) = cos(x):

1. Horizontal stretching:
Multiply the x-values by 1/4. This gives us f(x) = cos(1/4 * x).

2. Vertical shifting:
Add 1 to the y-values. This gives us g(x) = cos(1/4 * x) + 1.

Therefore, the equation of the new function, g(x), after stretching the graph of f(x) = cos(x) horizontally by a factor of 4 and shifting it 1 unit up, is g(x) = cos(1/4 * x) + 1.

To stretch the graph of f(x) horizontally by a factor of 4, we need to multiply the x-coordinate of each point on the graph by 1/4.

The equation for the horizontal stretch of g(x) becomes: g(x) = cos(1/4 * x)

To shift the stretched graph 1 unit up, we add 1 to the function:

g(x) = cos(1/4 * x) + 1

So, the equation of the new function g(x) is g(x) = cos(1/4 * x) + 1.

g(x) = f(1/4 x)+1