Join thousands of students who trust us to help them ace their exams!
Multiple Choice
Determine if the function is an exponential function. If so, identify the power & base, then evaluate for x=4. f(x)=(−2)x
A
Exponential function, f(4)=16
B
Exponential function, f(4)=−16
C
Not an exponential function
0 Comments
Verified step by step guidance
1
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: Analyze the given function f(x) = (-2)^x. Here, the base 'a' is -2, which is negative.
Step 3: Recall that for a function to be considered exponential, the base 'a' must be a positive real number. Since -2 is negative, f(x) = (-2)^x does not meet the criteria for an exponential function.
Step 4: Evaluate the function at x = 4 to check consistency. Calculate f(4) = (-2)^4. This involves raising -2 to the power of 4.
Step 5: Conclude that since the base is negative, f(x) = (-2)^x is not an exponential function, and therefore, the correct answer is 'Not an exponential function'.