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Which of the following is an example of a parent function?

a) y=√c
b) y=3log(x)
c) 2/x
d) y=3x²

1 Answer

7 votes

Final answer:

Option y=3x² represents a quadratic parent function, which is the simplest form of a function in the quadratic family and serves as the basis for more complex functions in that family.

Step-by-step explanation:

The question asks to identify which of the given options is an example of a parent function. In the context of mathematics, parent functions are the simplest form of functions in their respective families and serve as the basis for more complex functions. Among the given options, y=3x² is an example of a quadratic parent function. This is because the quadratic parent function is typically written as y=x², and the option provided is a stretched version of this basic form (multiplied by 3). On the other hand, options such as y=√(c), y=3log(x), and 2/x represent functions that are not in their simplest form and hence are not parent functions. Furthermore, option (d) fits the description from Figure 1.28 of an exponential relationship, which indicates that exponential functions have an entirely different structure and are not quadratic.

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