7-2 Graphing Exponential Functions Today’s Objective: I can graph any exponential function.

f and g are exponential functions with the same base. The graph of g is a ______ of the graph of f . compression reflection translation none of the above Justify your reasoning g f

Parent Function: 𝑦= 𝑏 𝑥 𝑦=𝑎⋅ 𝑏 𝑥 𝑦=𝑎⋅ 𝑏 𝑥−ℎ +𝑘 Stretch or compress Right/Left (h) Up/Down (k) (1+h, ab+k) (1, ) ab (h, a+k) (0, ) a (1, ) (0, ) 1 b 𝑦=𝑘 To Graph: Plot: y-intercept: (0, a) Plot: 2nd Point: (1, ab) Translate points and asymptote Asymptote y = k

𝑦= 2 𝑥 𝑦= 3⋅2 𝑥 y-intercept: 2nd Point: Translate: Asymptote: (0, 1) 𝑦=𝑎 ⋅𝑏 𝑥−ℎ +𝑘 To Graph: Plot: y-intercept: (0, a) Plot: 2nd Point: (1, ab) Translate points and asymptote Asymptote y = k 𝑦= 3⋅2 𝑥 y-intercept: 2nd Point: Translate: Asymptote: (0, 1) y-intercept: 2nd Point: Translate: Asymptote: (0, 3) (1, 2) (1, 6) none none 𝑦=0 𝑦=0 Domain: Range: All Real #s 𝑦>0 Domain: Range: All Real #s 𝑦>0

𝑦= −2(4) 𝑥 𝑦= 1 2 ⋅4 𝑥 y-intercept: 2nd Point: Translate: Asymptote: 𝑦= 1 2 ⋅4 𝑥 𝑦= −2(4) 𝑥 𝑦=𝑎 ⋅𝑏 𝑥−ℎ +𝑘 To Graph: Plot: y-intercept: (0, a) Plot: 2nd Point: (1, ab) Translate points and asymptote Asymptote y = k y-intercept: 2nd Point: Translate: Asymptote: (0, −2) (0, 1 2 ) y-intercept: 2nd Point: Translate: Asymptote: (1, −8) (1, 2) none none 𝑦=0 𝑦=0 Domain: Range: All Real #s 𝑦<0 Domain: Range: All Real #s 𝑦>0

𝑦= 2 𝑥−3 𝑦= 2 𝑥 +2 y-intercept: 2nd Point: Translate: Asymptote: 𝑦=𝑎 ⋅𝑏 𝑥−ℎ +𝑘 To Graph: Plot: y-intercept: (0, a) Plot: 2nd Point: (1, ab) Translate points and asymptote Asymptote y = k 𝑦= 2 𝑥 +2 y-intercept: 2nd Point: Translate: Asymptote: (0, 1) (0,1) y-intercept: 2nd Point: Translate: Asymptote: (1, 2) (1, 2) → 3 ↑ 2 𝑦=0 𝑦=2 p.447: 7, 8, 11, 15, 16, 18, 20,21,38,39 Domain: Range: All Real #s Domain: Range: All Real #s 𝑦>0 𝑦>2

7-2 Graphing Exponential Functions Day 2 Today’s Objective: I can graph any exponential function.

𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑇𝑒𝑚𝑝 𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑇𝑒𝑚𝑝 The best temperature to brew coffee is between 195°F and 205°F. Coffee is cool enough to drink at 185°F. The table shows temperature readings from a sample cup of coffee. Model this relationship. Temp change per minute 4.2% Time (min) Temp (°F) 203 5 177 10 153 15 137 20 121 Temp less room temp (70°) 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑇𝑒𝑚𝑝 𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑇𝑒𝑚𝑝 133 107 83 67 51 0.80 𝑦=𝑎⋅ 𝑏 𝑥−ℎ +𝑘 0.78 𝑦= 133⋅ (0.96) 𝑥 +70 0.81 0.76 Average Temp change per 5 min. = 21% decrease

The best temperature to brew coffee is between 195°F and 205°F The best temperature to brew coffee is between 195°F and 205°F. Coffee is cool enough to drink at 185°F. The table shows temperature readings from a sample cup of coffee. Model this relationship. Graph on calculator: enter data: [STAT] Set window STAT PLOT: [2nd], [y =] [GRAPH] L1 Time (min) Temp (°F) 203 5 177 10 153 15 137 20 121 L2 𝑌 1 =133 (0.96) 𝑥 +70

Continuous growth or decay You have $3000 to invest for 10 years at 5% annual rate with your choice of compounding. (yearly, quarterly, continuously) Yearly: 𝐴 𝑡 =𝑎 1+𝑟 𝑡 𝐴 10 =3000 1+0.05 10 𝐴 10 =4,886.68 Continuously: 𝑦=𝑒 𝑦= 1+ 1 𝑥 𝑥 Quarterly: 𝐴 𝑡 =𝑎 1+ 𝑟 𝑛 𝑛𝑡 𝐴 10 =3000 1+ 0.05 4 4(10) 𝐴 10 =4,930.86 𝑒=2.718281828459 𝐴 𝑡 =𝑃 𝑒 𝑟𝑡 𝐴 10 =3000 𝑒 0.05∙10 𝐴 10 =4,946.16