Exponential Growth/Decay
What is the domain of an exponential function?
All real numbers.
In an exponential function, which value causes the graph to be reflected?
Negative a
What are log functions inverses of?
Exponential functions
State the transformations:
y=-4^(x-6)
Right 6 and reflected
A line that a graph approaches more and more closely but never crosses is called what?
Asymptote
How would you tell if a function is exponential decay?
0<b<1
b is less than 1 or a fraction
Which value represents the asymptote of an exponential function?
k
What is the range of the log function below:
y=-Log6(X+1)-2
All real numbers
State the transformations:
y=5Log3(x-9)-7
Right 9, stretched 5, down 7
What equals zero in a horizontal asymptote?
y
What is the y-intercept of the following function?
y=a(b)^x
(0,a)
What is the range of the function below:
y=-3^x+2
y<2
Write the equation of the asymptote of the log function below:
y=-Log6(x+1)-2
x=-1
State the transformations:
y=-(1/2)3^(x+2)+3
Left 2, compressed 1/2, reflected, up 3
What type of function has a vertical asymptote?
log function
Nico purchased a new car for $22,000. Each year it depreciates at a rate of 15%. What is its value after 6 years (round to the nearest penny)?
$8297.29
What is the equation of the asymptote of the function below?
y=4^x-5
y= -5
T/F: Every log function has the same parent function.
False
What is the range of the following function:
y=-3x-1+6
y<6
Felicity's Cupcake Shop had annual sales last year of $360,000. Her sales are increasing at a rate of 3.5% per year. Write an exponential function to determine the sales after 5 years.
**WRITE A FUNCTION ONLY DO NOT SOLVE**
y=360,000(1+.035)5
OR
y=360,000(1.035)5
Austin made an investment of $6,000 at an interest rate of 6.5% compounded continuously. Find the value after 8 years (round to the nearest penny).
$10,092.17
Write the equation of a function to represent the parent function below if it were shifted left 2, reflected, and shifted up 3.
y=3^x
y=-3^(x+2)+3
Write the equation of a function to represent the parent function below if it were shifted left 5, stretched 4, reflected, and down 3.
y=Log3X
y=-4Log3(X+5)-3
What is the domain of the following function:
y=2Log3(x-8)-3
x>8
Mia purchased a laptop for $1500 in 2020. It loses its value by 32% each year. What is the value of the laptop today (round to the nearest penny)?
$471.65