Which of the following best describes the function ?
Table of contents
- 0. Functions7h 52m
- Introduction to Functions16m
- Piecewise Functions10m
- Properties of Functions9m
- Common Functions1h 8m
- Transformations5m
- Combining Functions27m
- Exponent rules32m
- Exponential Functions28m
- Logarithmic Functions24m
- Properties of Logarithms34m
- Exponential & Logarithmic Equations35m
- Introduction to Trigonometric Functions38m
- Graphs of Trigonometric Functions44m
- Trigonometric Identities47m
- Inverse Trigonometric Functions48m
- 1. Limits and Continuity2h 2m
- 2. Intro to Derivatives1h 33m
- 3. Techniques of Differentiation3h 18m
- 4. Applications of Derivatives2h 38m
- 5. Graphical Applications of Derivatives6h 2m
- 6. Derivatives of Inverse, Exponential, & Logarithmic Functions2h 37m
- 7. Antiderivatives & Indefinite Integrals1h 26m
- 8. Definite Integrals4h 44m
- 9. Graphical Applications of Integrals2h 27m
- 10. Physics Applications of Integrals 3h 16m
- 11. Integrals of Inverse, Exponential, & Logarithmic Functions2h 34m
- 12. Techniques of Integration7h 39m
- 13. Intro to Differential Equations2h 55m
- 14. Sequences & Series5h 36m
- 15. Power Series2h 19m
- 16. Parametric Equations & Polar Coordinates7h 58m
0. Functions
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 x=4.
f(x)=(−2)x
A
Exponential function, f(4)=16
B
Exponential function, f(4)=−16
C
Not an exponential function

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'.
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