7-2Graphing Exponential Functions

Today’s Objective:

I can graph any exponential function.

x

y

f and g are exponential functions with the same base.

The graph of g is a ______ of the graph of f .

A. compressionB. reflectionC. translationD. none of the above

Justify your reasoning

f g

x

y

x

y

(0, ) (1, )

Parent Function:

b

Stretch or compress Right/Left (h)Up/Down (k)

x

y

(0, )

ab(1, )

(h, a+k)

(1+h, ab+k)

𝑦=𝑘

To Graph:1. Plot: y-intercept: (0, a)2. Plot: 2nd Point: (1, ab)

3. Translate points and asymptote• Asymptote y = k

1a

𝑦=2𝑥 𝑦=3 ⋅2𝑥

To Graph:1. Plot: y-intercept: (0, a)2. Plot: 2nd Point: (1, ab)3. Translate points and

asymptote• Asymptote y = k

y-intercept:2nd Point:Translate:Asymptote:

(0 ,1)(1 , 2)

𝑦=0none

y-intercept:2nd Point:Translate:Asymptote:

(0 ,3)(1 , 6)

𝑦=0none

-5 5-5

5

x

y

-5 5-5

5

x

y

-5 5-5

5

x

y

Domain:Range: 𝑦>0

All Real #s

-5 5-2

8

x

y

-5 5-2

8

x

y

-5 5-2

8

x

y

Domain:Range: 𝑦>0

All Real #s

𝑦=− 2(4)𝑥 𝑦=12⋅ 4

𝑥

To Graph:1. Plot: y-intercept: (0, a)2. Plot: 2nd Point: (1, ab)3. Translate points and

asymptote• Asymptote y = k

y-intercept:2nd Point:Translate:Asymptote:

(0 ,− 2)(1 , −8)

𝑦=0none

y-intercept:2nd Point:Translate:Asymptote:

(0 ,12)

(1 , 2)

𝑦=0none

-5 5-10

2

x

y

-5 5-10

2

x

y

-5 5-10

2

x

y

-5 5-5

5

x

y

-5 5-5

5

x

y

-5 5-5

5

x

y

Domain:Range: 𝑦>0

All Real #s

Domain:Range: 𝑦<0

All Real #s

𝑦=2𝑥−3 𝑦=2𝑥+2To Graph:1. Plot: y-intercept: (0, a)2. Plot: 2nd Point: (1, ab)3. Translate points and

asymptote• Asymptote y = k

y-intercept:2nd Point:Translate:Asymptote:

(0 ,1)(1 , 2)

𝑦=0→ 3

y-intercept:2nd Point:Translate:Asymptote:

(0,1)(1 , 2)

𝑦=2↑ 2

-5 5-5

5

x

y

-5 5-5

5

x

y

-5 5-5

5

x

y

-5 5-5

5

x

y

Domain:Range: 𝑦>0

All Real #s

-5 5-5

5

x

y

-5 5-5

5

x

y

-5 5-5

5

x

y

-5 5-5

5

x

y

Domain:Range: 𝑦>2

All Real #s

p.447: 7, 8, 11, 15, 16, 18, 20,21,38,39

7-2Graphing Exponential Functions

Day 2

Today’s Objective:

I can graph any exponential function.

Time (min)

Temp (°F)

0 203

5 177

10 153

15 137

20 121

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 less room temp (70°)

133

107

83

67

51

𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑇𝑒𝑚𝑝𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠𝑇𝑒𝑚𝑝

0.80

0.78

0.81

0.76

Average Temp change per 5 min. = 21% decrease

Temp change per minute 4.2%

𝑦=𝑎 ⋅𝑏(𝑥−h )+𝑘𝑦=¿133 ⋅(0.96 )𝑥+70

Continuous growth or decayYou have $3000 to invest for 10 years at 5% annual rate with your choice of compounding. (yearly, quarterly, continuously)

Yearly:

Quarterly:

𝑦=(1+ 1𝑥 )

𝑥

5

5

x

y

𝑦=𝑒

𝑒=2.718281828459

Continuously: