Transformations
Exponential Function Graphing
Properties of Exponential Functions
Solving Exponential Equations
Exponential Equations Cont.
100
y=2x+5+6
Left 5, Up 6
100
What is the domain of an exponential function?
All real numbers
100
x5y2 x 3x3y4
3x8y6
100
4x=32
x=2.5
100
The population of Blue Ridge is growing at a rate of 5.4% per year. There are currently 2,000 people in town. What is the equation used to express the growth rate? How many people will there be in 10 years?
2,000(1+0.054)t
About 3,384 people will be in town in 10 years.
200
y=(1/2)(4)x-7-3
Right 7, Down 3
200
What is the asymptote of the function? y=4x+2-3
y=-3
200
12x7y3/3x2y4
4x5/y
200
9x+2=27-x
x=(-4/5)
200
Amanda and April both invest $200. Amanda invested in an account that will earn $8 each month. April invested in an account that will earn 5% interest every month. How much more money will April have than Amanda after one month?
April will have $2 more.
300
y=6x-2+3
Right 2, Up 3
300
What is the range of the function? y=(1/2)(8)x-5
y>-5
300
(2x3y5)4
16x12y20
300
125x=25
x=(2/3)
300
The graphs of a linear f(x) and exponential g(x) are shown. What are the values of F(2) and G(2)?
F(2) = 5, G(2) = 4
400
y=-3x+4-5
Reflection over the x-axis, Left 4, Down 5
400
What is the y-intercept of an exponential function? y=bx
(0,1)
400
6x-3y2
6y2/x3
400
216x-8=2-6
x=(1/8)
400
The number of bacteria increases by 15% each hour. If there were initially 600 bacteria, what is the function that can be used to determine the number of bacteria in x hours?
y=600(1.15)x
500
y= 5x+2+4
Left 2, Up 4
500
What is the y-value when x =-1 for the equation y=4x+2+1
y=1.25
500
(9x5y)0
1
500
24x-2=26
x=2
500
Given that the graph represents F(x), what is F(2)?
F(2)=-3