Suppose f(x) = x2 and g(x) = (12𝑥)2( 21 x) 2 . Which statement best compares the graph of g(x) with the graph of f(x)?A.The graph of g(x) is horizontally compressed by a factor of 2.B.The graph of g(x) is horizontally stretched by a factor of 2.C.The graph of g(x) is shifted 2 units to the right.D.The graph of g(x) is vertically compressed by a factor of 2.
Question
Suppose f(x) = x2 and g(x) = (12𝑥)2( 21 x) 2 . Which statement best compares the graph of g(x) with the graph of f(x)?A.The graph of g(x) is horizontally compressed by a factor of 2.B.The graph of g(x) is horizontally stretched by a factor of 2.C.The graph of g(x) is shifted 2 units to the right.D.The graph of g(x) is vertically compressed by a factor of 2.
Solution
The function g(x) = (12x)^2 * (2x)^2 can be simplified to g(x) = 576x^4. Comparing this to f(x) = x^2, we can see that the exponent of x in g(x) is twice as large as that in f(x). This means that the graph of g(x) is not a simple transformation (like a shift or stretch) of the graph of f(x). Instead, the graph of g(x) will be a different shape entirely. Therefore, none of the given options A, B, C, or D are correct.
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