The rule for the function g(x) is:
g(x) = 1.15*(x^2 - 3x -16)
How to write a rule for the function g?
First we know that the function f(x) is f(x) = x^2 - 7x
And we know that h(x) is a translation of 6 units down and 2 units to the left of f(x), then:
h(x) = f(x + 2) - 6
Now we know that g(x) is 115% of h(x), then we can write:
g(x) = 1.15*h(x)
Replacing h(x) by the rule above we get:
g(x) = 1.15*(f(x + 2) - 6)
Replacing the actual function there:
g(x) = 1.15*( (x + 2)^2 - 7*(x + 2) - 6)
g(x) = 1.15*( x^2 + 4x + 4 - 7x - 14 - 6)
g(x) = 1.15*(x^2 - 3x -16)
This is the rule for function g(x).
If you want to learn more about transformations:
https://brainly.com/question/4289712
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