The equation of the function f(x) is C. f(x) = x⁴ - x² + 3.
What is Translation of Functions?
Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.
There are horizontal translation and vertical translation of functions.
Given parent function is,
g(x) = x⁴ - x²
It is given that the function f(x) has the same shape as g(x).
f(x) is vertically translated.
From the graph, the points on f(x) is shifted 3 units to the up.
A function f(x) when undergoes vertical translation becomes f(x) ± k, where k is the units for which the translation occurs.
If the translation is done up to k units, function is f(x) + k.
f(x) = g(x) + 3 = x⁴ - x² + 3
Hence the function is f(x) = x⁴ - x² + 3.
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