Exponential Functions and Their Graphs

2 Exponential Function Families We’ve already learned about –This is the parent function We’ll expand this to –Note a=1 and h=0 in the parent function

3 ComponentProperty + kVertical shift up - kVertical shift down - hHorizontal shift to the right + hHorizontal shift to the left a > 1Stretch a < 1Compression -aReflection

4 The graph of f(x) = a x, a > 1 y x (0, 1) Domain: (– ,  ) Range: (0,  ) Horizontal Asymptote y = 0 Graph of Exponential Function (a > 1) 4 4

5 The graph of f(x) = a x, 0 < a < 1 y x (0, 1) Domain: (– ,  ) Range: (0,  ) Horizontal Asymptote y = 0 Graph of Exponential Function (0 < a < 1) 4 4

6 Example: Sketch the graph of f(x) = 2 x. x xf(x)f(x)(x, f(x)) -2¼(-2, ¼) ½(-1, ½) 01(0, 1) 12(1, 2) 24(2, 4) y 2–2 2 4 Example: Graph f(x) = 2 x

7 Example: Sketch the graph of g(x) = 2 x – 1. State the domain and range. x y The graph of this function is a vertical translation of the graph of f(x) = 2 x down one unit. f(x) = 2 x y = –1 Domain: (– ,  ) Range: (–1,  ) 2 4 Example: Translation of Graph

8 Example: Sketch the graph of g(x) = 2 -x. State the domain and range. x y The graph of this function is a reflection the graph of f(x) = 2 x in the y- axis. f(x) = 2 x Domain: (– ,  ) Range: (0,  ) 2 –2 4 Example: Reflection of Graph

9 The graph of f(x) = e x y x 2 – xf(x)f(x) Graph of Natural Exponential Function f(x) = e x

10 The irrational number e, where e  … is used in applications involving growth and decay. The number e

11 Pert

12 Continuously Compounded Interest

13 Pert Example Suppose you won a contest at the start of 5 th grade that deposited $3000 in an account that pays 5% annual interest compounded continuously. How much will you have in the account when you enter high school 4 years later? Express the answer to the nearest dollar.