daily question how does one graph an exponential equation?
TRANSCRIPT
Daily Question
How does one Graph an Exponential
Equation?
It’s an Exponential Growth Function when…
x hy kba
b is greater than1OR
if the exponent is negative and it flips b and b is greater than 1
It’s an Exponential Decay Function when…
x hy kba
b is a fraction (greater than 0 and less than 1)
OR
if the exponent is negative and it flips b and b is less than 1
State whether f(x) is an exponential growth or exponential decay
21.
3
52.
4
3. 6
x
x
x
f x
f x
f x
DECAY
GROWTH
GROWTH
State whether f(x) is an exponential growth or exponential decay
14. 4
3
35. 5
4
6. 2 0.15
x
x
x
f x
f x
f x
DECAY
GROWTH
DECAY
Transformations
x hy ka b
Describe the transformation.
1
47. 2
3
8. 2 5
59.
3
x
x
x
f x
f x
f x
Up 2
Down 5
Left 1
Describe the transformation.
310. 5
11. 2
12. 3 2 2
x
x
x
f x
f x
f x
Right 3
Reflect across the x-axis (flips)
Up 2
Domainand
Range
DomainALL REAL
,
RangeUse k
x hy ka b If a is positive use If a is negative use
k,
,k
Identify the domain and range.
3
20. 2 4
21. 3 2
22. 4 1
x
x
x
f x
f x
f x
D:
R:
D:
R:
D:
R:
,
,
,
,4
0,
1,
Asymptote
• A line that a graph approaches but will never touch
• Horizontal, Dashed line
x hy ka b
y = k
Identify the asymptote of the graph of the function.
2
2
13. 3 4
14. 4 3
115. 5
2
x
x
x
f x
f x
f x
y = 4
y = -3
y = 0
the x-axis
X-Int:(#, 0) - Where the graph crosses the x-axis
Y-Int:(0, #) - Where the graph crosses the Y-axis
Read from left to right!
Increasing:
up from left to right
Decreasing:
down from left to right
End Behavior
x _____, f x _____
x _____, f x _____
Domain Range{ }
Let’sPractice