1. UNIT 5: Graphing Exponential Functions
a = original amount (y-intercept)
b = growth factor (1 ± r)
r = rate (percent)
y = final amount
x = unit of measure (time, bounces, etc.)
Exponential Growth
Exponential Decay
End Behavior:
End Behavior:
Math 3 Hon: Unit 5

2. Things to know about b cannot be negative b > 1: 0 < b < 1:
DOMAIN of all exponential functions is: all real numbers (no restrictions for x)
RANGE of exponential functions: Positive “a” Negative “a”
Y – INTERCEPT = a
y-values follow multiply or divide patterns

3. Identifying Growth & Decay: What is the factor v. rate?b) c) d) e) f)

4. Graphing Exponentials (Unshifted) by Hand:
Find y-intercept, domain, range, and SKETCH 1. 2. 4. 3.

5. Write Unshifted Exponential Equation by Hand:
Given two points of the exponential graph
1. (0, 3) and (1, 5)
2. (0, -2) and (-1, -8)
3. (0, 7) and (2, 63)
4. (0, 56) and (3, 7)

6. Graphing Shifted Exponential Functions by Hand:
Original :
Shifted: x y -2 or -1 a 1 ab 2
ab2
“h”:
“k”:
Shifted DOMAIN:
Shifted RANGE:

7. Graphing Shifted Exponential Functions by Hand:
1. Describe the Shift: (Up, Down, Left, Right)
2. Describe the Shift: (Up, Down, Left, Right)
Original Function and Key Points:
Shifted Points:
Original Function and Key Points:
Shifted Points:
3. Describe the Shift: (Up, Down, Left, Right)
4.Describe the Shift: (Up, Down, Left, Right)

8. Solving for the vertical shift value (k) of an exponential:
Substitute and solve
Given: y = 4(2)x + k
Given: y = 16(1/2)x + k
Given: y = 3x + k
(-1, 5)
(2, 2)
(0, 4)
Given:
Given:
(2, 6)
(-1, -1)