Multiple Choice
Determine if the function is an exponential function.
If so, identify the power & base, then evaluate for .
6. Exponential and Logarithmic Functions
Introduction to Exponential Functions
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple 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^x, where 'a' is a positive constant and 'x' is the variable exponent.
Step 2: Examine the given function f(x) = (-2)^x. Here, the base is -2, which is not a positive constant. This violates the condition for a function to be exponential.
Step 3: Consider the implications of having a negative base. When the base is negative, the function does not exhibit the typical properties of exponential growth or decay, especially for non-integer values of x.
Step 4: Evaluate the function for x = 4. Substitute x = 4 into f(x) = (-2)^x to get f(4) = (-2)^4. Calculate the result to understand the behavior of the function.
Step 5: Conclude that since the base is negative, the function f(x) = (-2)^x is not an exponential function according to the standard definition.
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