The graphs of f(x) and g(x) are shown below:
graph of function f of x open upward and has its vertex at negative 7, 0. Graph of function g of x opens upward and has its vertex at negative 9, 0.
If f(x) = (x + 7)2, which of the following is g(x) based on the translation?
g(x) = (x + 9)2
g(x) = (x + 5)2
g(x) = (x − 9)2
g(x) = (x − 5)2
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The introduction to this problem essentially summarizes an important property of functions: if f(X) plots a function, then f(X+A) plots the same function shifted to the left A units. Likewise, if f(X) plots a function, then f(X-A) plots the same function shifted to the right A units.
You are given that f(X) = (X+7)^2 and that the function given by f(X) = (X+7)^2 has a vertex at (-7,0). If you recall the graph of f(X) = X^2, the function has a vertex at (0,0). Thsi means that when f(X) becomes f(X+7), the graph is shifted to the left 7 units. So logically following, what would the g(X) have to be to shift the graph to the left 9 units?