Polynomial and Rational Functions
What's the instantaneous rate of change?
The ROC at one instant point, the tangent line. of a singular point, etc.....
The inverse of an exponential equation is a ____.
LOG!
On the unit circle, what direction causes the angles to be negative?
Clockwise
Polar functions input ____ and output _____.
(theta, radius)
secx is equal to what?
1/cosx
What's the end behavior of a function with a positive leading coefficient and an odd degree? (Limit notation plz)
logb(x/y)
Where does the graph of sine start with no transformations?
At the origin
How many petals are in the function r=5sin(4θ)
8 petals
Period of cotangent
π
A VERTICAL ASYMPTOTE
logs can be used to model situations where the inputs grow ____ and the outputs grow ____.
multiplicatively, additively
What is the range of arccosx?
[0,π]
For r = a+bcosθ, and |a|<|b|, what shape is the limacon?
Loop
Name one pythagorean identity
sin2θ+cos2θ=1
1+cot2θ=csc2θ
tan2θ+1=sec2θ
Linear equations have a constant ____ of ____, quadratic equations have a constant ____, and geometric sequences have a ___ _____.
Rate of Change, 2nd Difference, common ratio
If logbx=logby, then what?
x=y
Where is tanθ undefined?
When θ = Π/2 +kΠ
For r = a+bcosθ, and |a|=|b|, what shape is the limacon?
Cardiod
Difference of angles that equals 7π/12
(60°+45°) ->105°
What's the horizontal asymptote of this equation:
y = (4x2+2)/(5x2+17)
y = 4/5
Formula for continuously compounded interest for P(t).
P(t) = P0ert
What is the angle sum identity for cos(α + β)?
cos(α + β)=cos(α)cos(β)-sin(α)sin(β)
With the equation r=4sin(3θ), where are the petals on the unit circle?
(4,π/6) , (4,5π/6), (4,3π/2)
Give the steps, in order, to create the inverse of an equation.
1. replace f(x) with y
2. switch x and y
3. solve for y
4. rewrite the function as f-1(x)