Lindsay882
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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)= ?

Respuesta :

The equation of the new function is [tex]g(x)= cos4 x+1[/tex]

Explanation:

The Parent function is [tex]f(x)=cos x[/tex]

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

[tex]f(x)=a \cos b(x-c)+d[/tex]

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, [tex]b=4[/tex] and [tex]d=1[/tex]

Substituting these values in the formula, we have,

[tex]g(x)=cos4x+1[/tex]

Thus, the equation of the new function is [tex]g(x)= cos4 x+1[/tex]

facundo3141592

The transformed function will be:

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

How to get the equation of the transformed function?

First, we need to describe the two transformations used here, these are:

Horizontal stretch:

For a given function f(x), an horizontal stretch of scale factor k is written as:

g(x) = f(x/k)

Vertical shift:

For a given function f(x), a vertical shift of N unis is written as:

g(x) = f(x) + N

  • If N is positive, the shift is upwards.
  • If N is negative, the shift is downwards.

Here we have:

"... stretching it horizontally by a factor of 4 and shifting it 1 unit up."

Then:

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

By replacing f(x) we get:

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

If you want to learn more about transformations, you can read:

https://brainly.com/question/4289712