For the following pair of functions, the vertex of g(x) 2 units to the right of f(x),
f(x) = x² and g(x) = (x - 2)²
What are functions?
Defining a relationship between an independent variable and a dependent variable using mathematical expressions, rules, or laws is known as a function. Mathematics is rife with functions, and the sciences depend on them for constructing physical relationships.
Determining the Correct Pair of Functions
For a given function f(x), its horizontal translation would be f(x + a). Here, a is the distance translated, owing to which f(x + a) is generated.
If a > 0, then it indicates a right translation of a units.
If a < 0, then it indicates a left translation of a units.
The required functions are to be such that the vertex of g(x) is 2 units to the right of the vertex of f(x).
Thus, if f(x) = x², then g(x) = (x - 2)²
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no solutions in real numbers.