W6: Inverse Function
Using the formula A(t) = ae^rt, what is the value of an investment with an initial value (indicated by the variable a) of $1,000 that continuously compounded at 8% (r) over 50 years (t)? (Use 2.718 for the value of e.)
$54,576
What is the value of log low3(1)? (Enter DNE to indicate does not exist.)
0
What is the value of log(1)?
0
What is the value of ln(e)?
1
Evaluate the power function f(x) = 2^x when x = -3
1/8
Decibels are a measure of sound on a logarithmic scale, where the number in front of the zero represents the number of powers of 10 (can think of as the number of zeros). As an example, a whisper is around 10 dB (power ratio of 10 / 1 zero) while a jet engine is around 120 dB (power ratio of 1,000,000,000,000 / 12 zeros). Convert the value of a washing machine at 80 decibels into a power ratio.
100,000,000
Simplify 2ln(x^3) -3ln(x)
ln(x^3)
Expand log(2x/5)
log(2) + log(x) -log(5)
Which of the answer choices is equal to log lower 3 (6)?
log(6)/log(3)
Which of the following is equal to log(xy)?
log(x) + log(y)
Which of the following is equal to log(y/x)?
log(y) - log(x)
If f(x) = log low3(x), what is the transformation that occurs if g(x) = -log low3(x)? (Enter s for stretch, c for compress, mx for mirrored across the x-axis, my for mirrored across the y-axis, r for shift right, l for shift left, u for shift up, and d for shift down.)
mx
Are f(x) and g(x) inverse functions if f(x) = 2x + 2 and g(x) = -2x -2? (Give your answer as yes or no.)
no
In the power function f(x) = -4x^3, what is the end behavior of f(x) as x goes to -∞? (You can enter pi for positive infinity and ni for negative infinity.)
pi
What is the end behavior of f(x) in the function f(x) = log(x) as x goes to infinity? (You can enter pi for positive infinity and ni for negative infinity.)
pi
If f(x) = ln(x), what is the transformation that occurs if g(x) = ln(x - 5)? (Enter s for stretch, c for compress, r for shift right, l for shift left, u for shift up, and d for shift down.)
r
What is the domain of the function f(x) = log(x)?
x > 0
What is the domain of the inverse function of f(x) = x^2? (If the domain is all real numbers, you can write x = R.)
x ≥ 0
What is the domain of the inverse function of f(x) = x^3?
x= R
What is the range of the inverse function of f(x) = square root of x?
f(x) greater than or equal to 0
Evaluate f(x)= 4x^2 when x = 3
f(x)= 4(3)^2 4(9)= 36 36
What is the inverse function of f(x) = 3x- 2?
f^-1(x) = x+2/3
What is the inverse function of f(x) = 2x?
f^-1(x)= x/2
What is the inverse function of f(x) = x/3 - 5? (Use g(x) to represent the inverse function)
g(x)=3x+15
What is the inverse function of f(x) = x + 2? (Use g(x) to represent the inverse function)
g(x)=x-2
What is the value of log lower5 (1/25)?
-2
The function of f(x) = 3x + 2 has a domain of -3 < x < 5. What is the range of f^-4(x)?
-3 < f(x) < 5
What is the value of log low2(1/32)?
-5
The function of f(x) = 3x + 2 has a domain of -3 < x < 5. What is the domain of f^-1(x)?
-7 < f(x) <17
If a virus spreads at a rate that can be modeled by the exponential function A(t) = ae^rt, how many people will be infected after 5 days if initially 3 people are infected and the growth rate is 40%? (Use your calculator for a precise version of e. If you are not able to use a calculator, you can approximate e as 2.718. Round your answer to the nearest person.)
22
Which of the following is equal to log(p^2)?
2log(p)
Simplify the expression log(2x) + log(x) - log(2)
2log(x)
In the exponential function f(x) = 2^-x+ 3, what is the end behavior of f(x) as x goes to ∞? (You can enter pi for positive infinity and ni for negative infinity.)
3
What is the value of log low4(64)? (Enter DNE to indicate does not exist.)
3
What is the value of log(1,000)
3
What is the value of x in the equation 2^9 = 2^3x?
3
Solve for x in the equation log lowx (64) = 3
4
What is the value of log low3, (81)?
4
What is the value of x in the equation 3^8= 9^x
4
Simplify the expression log low3(90). \ (Round your answer to the nearest tenth. Also, you can use the value 2.1 for log(10)/log(3))
4.1
Simplify the logarithm: log lower 3(81^2)
8
If f(x) = log(x), what is the transformation that occurs if g(x) =1/3 log(x) - 1?
Compressed and shifted down.
What type of function is f(x)=3^x?
EXPONENTIAL
What is the range of the function f(x) = log(x)?
f(x) = R
For x < 0, which answer best describes the curve of the function f(x) = -2^-x
Negative values of f(x); flat near 0, but steepening as x approaches -∞
What type of function is f(x) = x^2?
POWER
For x > 0, which answer best describes the curve of the function f(x) = x^2?
Positive values of f(x); flat near 0, but steepening as x approaches ∞
For x > 0, which answer best describes the curve of the function f(x) = x^1/2
Positive values of f(x); steep near 0, but flattening as x approaches ∞
If f(x) = log(x), what is the transformation that occurs if g(x) = log(x - 3)?
Shifted to the right
If f(x) = log(x), what is the transformation that occurs if g(x) = log(x) + 1?
Shifted up
If f(x) = log(x), what is the transformation that occurs if g(x) = 2log(x)?
Stretch
