Key Features Expon. f(x)'s
Growth or Decay
Growth or Decay 2
Transformations
Transformations 2
100
Given the equation,
y = 3(2)x, what is the domain and range?
domain: all real numbers
range: y > 0
100
Is the following function growth or decay:
f(x)=7(3/2)^(x-2)
Growth
100
A bunny population doubles every 6 months. The starting population is 10 and their growth can be modeled using the exponential function y = 10(2)t.
What is the bunny population for t = 3?
80
100
What is the parent function of the exponential?
y=(4/5)^{x+2}
y = (4/5)x
100
In an exponential function, what happens when h is a negative number?
f(x)=-a(b)x-h+k
The graph shifts right "h" units
200
What is the asymptote for the function
f(x) = 2(3)x-1+4?
y = 4
200
Is this function growth or decay?
y = 3(1.5)x
growth
200
In exponential functions, when b>1 this will cause an exponential growth or decay?
Exponential growth
200
What transformation of the exponential function?
y=(1.3)^x - 4
Shift down 4
200
Create an exponential function that reflects over the x-axis and has an asymptote at y=-3.
-(2)^(x+5)-3
300
What is the range for this exponential function?
y > 0
300
f(x)=a(.93)x
Does this functions represent exponential growth or decay?
Exponential Decay by 7%
300
f(x)=a(1.07)x
Does this functions represent exponential growth or decay?
Exponential Growth. 7%.
300
Name both transformations to the exponential function.
y=3(0.01)^{x-2}
shift right 2
vertical stretch of 3
300
List the transformations in the following exponential function:
f(x)= -1/3(7)^(x+5)-1
Reflection over the x-axis
Vertical shrink by 1/3
Shift left 5 units
Shift down 1 unit
400
What is the domain for the function displayed in the table?
all real numbers
400
How much would I need to add to "b" to change this function from decay to growth?
y = 4(0.5)x
0.5
400
What is the asymptote of the graph below?
y = 0 (x-axis)
400
Is this a vertical stretch or a vertical compression? How do you know?
y=1/2(1.7)^x
Compression - 1/2 < 1
400
Create an exponential function that has a vertical stretch, shifts right three units, and shifts up four units.
f(x)=7(6)^(x-3)+4
500
What is the difference between linear functions and exponential functions?
Linear has a constant rate of change.
Exponential has a FACTOR.
500
Finish the statements,
If b > 1, the function exhibits exponential ________.
If 0 < b < 1, the function exhibits exponential ________.
growth
decay
500
Annual sales of a Wingstop franchise are $530,000 and increasing at a rate of 5%.
The function is S = 530,000(1.05)t
What will the annual sales be in 6 years?
530,000(1.05)6 = $710,250.69
500
Name all 4 transformations on the exponential function.
y=-6(1.33)^{x+4}-5
reflection over the x-axis
shift left 4
shift down 5
vertical stretch of 6
500
If g(x) is a transformation of f(x), then what transformations occur?
f(x) = bx
g(x) = 3f(x)+4
Vertical stretch of 3 units
Shift up 4 units