The function g(x) is a transformation (flipped upside down and horizontally stretched) of the quadratic parent function, f(x) = x2. g(x) = -0.5x².
What is flipping upside down?
Flipping upside down, is found by taking the negative of the original function; that is, the rule for this transformation is −f (x).
Since, g(x) is an upside down function of f(x), g(x) = -f(x).
What is stretching a graph?
If we multiply a function by a coefficient, the graph of the function will be stretched.
A function h(x) represents a horizontal compression of f(x) if h(x) = f(cx) and c > 1.
A function h(x) represents a horizontal stretch of f(x) if h(x) = f(cx) and 0 < c < 1.
Since, g(x) is clearly a stretched transformation of f(x), c < 1.
The possible function g(x) = -0.5x².
Learn more about stretching a graph here
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