Fill in the blank(s) to correctly complete each sentence. If ƒ(x) = 4^x, then ƒ(2) = and ƒ(-2) = ________.

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Identify the given function: $f(x) = 4^x$, which means the function raises 4 to the power of $x$.

To find $f(2)$, substitute $x = 2$ into the function: $f(2) = 4^{2}$.

Calculate the expression \$4^{2}$ by multiplying 4 by itself twice (though we won't compute the final value here).

To find $f(-2)$, substitute $x = -2$ into the function: $f(-2) = 4^{-2}$.

Recall that a negative exponent means taking the reciprocal: $4^{-2} = \frac{1}{4^{2}}$. This completes the expression for $f(-2)$.

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주요 개념

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Exponential Functions

An exponential function has the form f(x) = a^x, where the base a is a positive constant. The function grows or decays depending on the base, and the exponent x can be any real number. Understanding how to evaluate these functions at specific values of x is essential.

Evaluating Functions at Given Inputs

To find f(c) for a function f(x), substitute the input value c into the function in place of x. This process involves performing the necessary arithmetic operations to simplify and find the output value corresponding to the input.

Negative Exponents

A negative exponent indicates the reciprocal of the base raised to the positive exponent, i.e., a^{-n} = 1 / a^n. This rule is crucial when evaluating exponential functions at negative inputs, ensuring correct calculation of values like f(-2).

Fill in the blank(s) to correctly complete each sentence. If ƒ(x) = 4x, then ƒ(2) = and ƒ(-2) = ________.