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Identify the function as a power function, a polynomial function, or neither.

f(x)=4(x^3)^3

User Bertucho
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2 Answers

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Answer:7

Step-by-step explanation:7

User Iskar Jarak
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7 votes

Final Answer:

f(x) = 4(x^3)^3 is a power function.

Step-by-step explanation:

A function is considered a power function if it can be expressed in the form:

f(x) = a * x^n

where:

a is a real number coefficient (can be positive, negative, or zero)

n is a real number exponent (can be any real number)

x is the independent variable

In the case of f(x) = 4(x^3)^3:

a = 4

n = 3 raised to another power (3^3 = 27)

Therefore, f(x) can be rewritten as:

f(x) = 4 * x^(3^3)

Matching the general form of a power function confirms that f(x) is indeed a power function.

Here's a simple way to remember:

If the variable is raised to a single fixed exponent, it's a power function.

If the variable has multiple exponents or is involved in arithmetic operations with other terms, it's not a pure power function.

In this case, even though the exponent itself is raised to another power, the variable (x) remains in the same basic form (x raised to a fixed exponent). Therefore, f(x) qualifies as a power function.

User Nazim Faour
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