The value k needed for the transformation of f(x) to g(x) = f(k · x) is equal to 3.056.
<h3>How to find the find the dilation factor</h3>
In this problem we have the following relationship bewteen the two <em>quadratic</em> equations: g(x) = f(k · x), which means that for all y the following relationship between f(x) and g(x):
Let suppose that y = 3, then and
, then the value k is:
k = (- 5.5)/(- 1.8)
k = 3.056
The value k needed for the transformation of f(x) to g(x) = f(k · x) is equal to 3.056.
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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 .