0. Functions

Common Functions

0. Functions

Common Functions

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Multiple Choice

Determine if the function is an exponential function.
If so, identify the power & base, then evaluate for $x=4$ .
$f\left(x\right)=\left(-2\right)^{x}$

Exponential function, $f\left(4\right)=16$

Exponential function, $f\left(4\right)=-16$

Not an exponential function

Verified step by step guidance

Step 1: Understand the definition of an exponential function. An exponential function is of the form f(x) = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number not equal to 1), and 'x' is the exponent.

Step 2: Analyze the given function f(x) = (-2)^x. Here, the base is -2, which is a negative number. Recall that for a function to be exponential, the base must be a positive real number.

Step 3: Conclude that since the base (-2) is negative, the given function does not meet the criteria for an exponential function.

Step 4: Note that evaluating f(4) = (-2)^4 would result in a positive value (16), while evaluating f(4) = (-2)^4 with a negative base raised to an odd power would result in a negative value. This inconsistency further supports that the function is not exponential.

Step 5: Final conclusion: The given function f(x) = (-2)^x is not an exponential function because the base is negative, which violates the definition of an exponential function.