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.