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UNO [17]
3 years ago
13

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)= ?
Mathematics
1 answer:
SpyIntel [72]3 years ago
8 0

The equation of the new function is g(x)= cos4 x+1

Explanation:

The Parent function is f(x)=cos x

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

f(x)=a \cos b(x-c)+d

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, b=4 and d=1

Substituting these values in the formula, we have,

g(x)=cos4x+1

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

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