Exponential & Logarithmic Functions
What is the inverse for natural log?
e
The numerical value of sin(3pi/2) + cos(pi/4) is
- 1 + sqrt(2)/2
What is the standard form for a rational function?
f(x) = a + b/x - c
What formula is used to find the minimum of a sinusoidal function?
k - A
What is the difference between exponential and logarithmic growth?
Exponential increases really fast, while log grows slowly
What is the standard form for a sinusoidal function?
f(x) = Asin(b(x - h)) + k
Consider the function: f(x)=3/(x-2) As x approaches infinity, what is the end behavior of f(x)?
f(x) approaches 0
How do you know which Law to use when finding a missing measurement of a triangle?
You can ONLY use the Law of Sines if there is a complete pair(side & angle)
Identify the x-intercept for f(x) = log(x - 4).
5
Analyze the sinusoidal model equation representing the average monthly temperatures for Celano: y=18.2sin(0.52x-2.1)+65.8 What are the highest and lowest temperatures?
84 and 47.6
What are the asymptotes of the function y=-3/(x+1) -2?
x=-1, y=-2
A Ferris wheel has a diameter of 80 feet. Riders enter the Ferris wheel at it's lowest point, 5 feet above the ground, at time t = 0 seconds. One complete rotation takes 65 seconds. What function models a rider's vertical height, h(t), at t seconds?
h(t) = - 40cos((2pi/65)t) + 45
A certain pain reliever is taken in 220 mg dosages and has a half-life of 12 hours. The function A=220(12)t/12 can be used to model this situation, where A is the amount of pain reliever in milligrams remaining in the body after t hours. According to this function, how much pain reliever is left after 12 hours?
In 12 hours, 110 mg of pain reliever is remaining
The terminal side of , an angle in standard position, intersects the unit circle at P(-1/3,-sqrt(8)/3). What is the value of sec x?
- 3
Given the function f(x)=(-3/5)x-9, if g(x) is the inverse of f(x), evaluate g(15).
- 40
What two values of x satisfy the equation sqrt(3 - 2cos x) = 2?
120o and 240o
Find all values of x for which ln(x2 - 2x - 2) = 0.
x = -1 and x = 3
The hours of daylight, y, in Utica in days, x, from January 1, 2013 can be modeled by the equation y=3.06sin(0.017x-1.40)+12.23. How many hours of daylight, to the nearest tenth, does this model predict for February 14, 2013? (Note: There are 31 days in January.)
10.4 hours
If f and g are two functions defined by f(x)=3x+5 and g(x)=x2+1, then g(f(x)) is
9x2+30x+26
Triangle ABC has the following measurements, m<A = 30o, m<C = 50o, and AC = 13 units. What is the length of side AB to the nearest tenth?
10.1 units