3.1. Exponential Functions http://www.ck12.org
Minimums: None
Asymptotes:y=0 asxgets infinitely small
Holes: None- Exponential functions are of the formy=a·bx
a.y=x^6 is not an exponential function becausexis not in the exponent.
b.y= 5 xExponential function.
c.y= 1 xNot a true exponential function becauseyis always 1 which is a constant function.
d.y=xxNot an exponential function becausexis both the base and power of the exponent.
e.y=x^12 Not an exponential function. - The starting number isa=3. This number is changed by a factor of^1 ewhich isb.
f(x) = 3 (^1 e)x= 3 e−x
Practice
- Explain what makes a function an exponential function. What does its equation look like?
- Is the domain for all exponential functions all real numbers?
- How can you tell from its equation whether or not the graph of an exponential function will be increasing?
- How can you tell from its equation whether or not the graph of an exponential function will be decreasing?
- What type of asymptotes do exponential functions have? Explain.
- Suppose you invested $4,500 and it grew by 4% every year for 30 years. How much would this investment be
worth after 30 years? - Suppose you invested $10,000 and it grew by 12% every year for 40 years. How much would this investment be
worth after 40 years?
Write the exponential function that passes through the following points. - (0, 5) and (1, 25)
- (0, 2) and (1, 8)
- (0, 16) and (2, 144)
- (1, 4) and (3, 36)
- (0, 16) and (3, 2)
- (0, 81) and (2, 9)
- (1, 144) and (3, 12)
- Explain why for exponential functions of the formy=a·bxthey-intercept is always the value ofa.