the graph of f(x), shown below, resembles the graph of g(x) = x2, but it has been changed somewhat. which of the following could be the equation of f(x)?

And, After seeing the given figure, we can say that the end behavior of f(x) is same as g(x). So, function f(x) must has even degree with positive leading coefficient.

Now, again according to the graph it seems f(x) is obtained by shifting g(x), 1 unit vertically downward.

And, also it is compressed by some unit less than 1.

So it is the type of [tex]f(x)=ax^2-1[/tex] where a is must be a positive number less than 1. ( because here vertical compression occurs)

Since, from the given options , only Option D is showing the above conditions.

Therefore Option D. [tex]f(x)=0.4x^2-1[/tex] is the correct function for the given graph.

topeadeniran2 topeadeniran2 · Answer 2 · 2022-03-23T17:32:27+01:00

The equation of f(x) from the graph is D. f(x) = 0.4x² - 1.

How to explain the equation?

From the information given, it was stated that the graph of f(x) resembles the graph of g(x) = x², but it has been changed.

In this case, it's appropriate for f(x) to have a positive coefficient. The graph also depicts that f(x) will be gotten by shifting the position of g(x).

In this case, it's also compressed by units less than 1. Therefore, the equation of f(x) from the graph is f(x) = 0.4x² - 1.

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