Multiple Choice
Determine if the function is an exponential function.
If so, identify the power & base, then evaluate for .
0. Functions
Exponential Functions
Multiple Choice
Determine if the function is an exponential function.
If so, identify the power & base, then evaluate for .
A
Exponential function,
B
Exponential function,
C
Not an exponential function
Verified step by step guidance1
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 (b > 0 and b ≠ 1), and 'x' is the exponent. The base must be a positive real number.
Step 2: Analyze the given function f(x) = (-2)^x. Here, the base is -2, which is a negative number. This violates the condition for an exponential function, as the base must be positive.
Step 3: Recognize that because the base is negative, the function f(x) = (-2)^x is not defined for all real values of x. For example, fractional exponents would result in complex numbers, which are not part of the domain of a standard exponential function.
Step 4: Conclude that the given function f(x) = (-2)^x does not meet the criteria for an exponential function due to the negative base.
Step 5: State the final conclusion: The function is not an exponential function, and therefore, there is no need to evaluate it for x = 4 or identify a base and power.
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