If f(x)=x^2 is vertically stretched by a factor of 9 to g(x). What is the equation of g(x)?

Given:

The function is:

This function is stretched by a factor of 9 to g(x).

To find:

The equation of function function g(x).

Solution:

The vertical stretch is defined as:

          ...(i)

If , then the function f(x) compressed vertically by factor k.

If , then the function f(x) stretched vertically by factor k.

The given function f(x) is stretched by a factor of 9 to g(x).  So the value of k is 9.

Substituting in (i), we get

Therefore, the required function is .

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step-by-step explanation: