Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient.
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
Common Functions
Struggling with Calculus?
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
Identify the general form of an exponential function, which is f(x) = a^x, where 'a' is a positive constant base and 'x' is the exponent.
Examine the given function f(x) = (-2)^x. Here, the base is -2, which is negative.
Recall that for a function to be considered exponential, the base 'a' must be a positive real number. Since -2 is negative, this function does not meet the criteria for an exponential function.
Evaluate the function at x = 4 to check the behavior: f(4) = (-2)^4. Calculate the power: (-2)^4 = 16, but this step is not necessary for determining if it's exponential.
Conclude that since the base is negative, f(x) = (-2)^x is not an exponential function.
Watch next
Master Graphs of Common Functions with a bite sized video explanation from Patrick
Start learningRelated Videos
Related Practice
Common Functions practice set
