1. 7-2 Graphing Exponential Functions
Today’s Objective:
I can graph any exponential function.

2. 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

3. 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

4. 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= ⋅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

5. 𝑦= −2(4) 𝑥 𝑦= 1 2 ⋅4 𝑥 y-intercept: 2nd Point: Translate: Asymptote:
𝑦= ⋅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

6. 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. 7-2 Graphing Exponential Functions Day 2
Today’s Objective:
I can graph any exponential function.

8. 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

9. 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

10. 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 =
𝐴 10 =4,886.68
Continuously:
𝑦=𝑒
𝑦= 𝑥 𝑥
Quarterly:
𝐴 𝑡 =𝑎 1+ 𝑟 𝑛 𝑛𝑡
𝐴 10 = (10)
𝐴 10 =4,930.86 𝑒=
𝐴 𝑡 =𝑃 𝑒 𝑟𝑡
𝐴 10 =3000 𝑒 0.05∙10
𝐴 10 =4,946.16