Vocabulary
A ________ is a relationship where every input has exactly one output
Function
Another term for Rate Of Change
Slope
What are logs and exponents to each other
2π
Vertex of y + 3 = 1/2(x - 2)2
(2, -3)
f(x) = 4(x - 4)3 - 2 is a _____ function
Cubic
Vertex of -(x + 3)2 + 5
(-3, 5)
If f(x) = 4x
Find the value for x if f(x) = 16
x = 2
tan(3π/4)
-1
Manipulate the hyperbola to set it equal to 1:
x2 - 4(y - 3)2 = 16
x2/16 - (y - 3)2/4 = 1
The unit used to measure angles in circles
Radians
Use limit notation to describe the end behavior of the following equation as x increases without bound:
f(x) = -(x - 6)3 + 8
lim f(x) = -∞
x -> ∞
lim f(x) = ∞
x -> -∞
Solve for x for the following equation: log3(x) = 3
x = 27
arccos(-1/2)
2π/3
Identify the conic type and point of interest(names included):
(x - 6)2/16 + (y - 3)2/16 = 1
Conic: Circle
Point Of Interest: Center (6, 3),
Exponential ______ and Exponential _____
Growth and Decay
Describe the graph of
(x - 2)2 + 4 where x < 2
Concave up, ROC negative and increasing
Solve for x: log3(x-7)= 5
x = 132
Find all possible values where sinθ = -√3/2
4π/3, 5π/3 + 2πk ,k∈Z
find the focus of the following parabola:
1/8(y - 3)2 = x - 4
(6, 3)
Match the conic template equations with their corresponding name
1: (x = h)2 + (y - k)2 = r2
2: y = a(x - h)2 + k
2: Parabola
Describe the following for the factored polynomial of
f(x) = (x + 6)(x - 2)2(x - 5)3:
Roots, Degree, Type of graph touch for each factor
Roots: x = -6, 2, 5
Degree = 6
Touches: x = -6: Cross, x = 2: Bounce, x = 5: Cross
Solve for x: log2(16x) - 10 = 2
x = 256
tan(3π/4 + π/6)
-√3/3
Find the following of the conic
(x + 4)2/36 + (y - 7)2/25 = 1
Identity, Center, Vertexes, and the a & b values
Identity: Horizontal Ellipse
Center: (-4, 7)
Vertexes: (-10, 7), (2, 7)
a = 6 b = 5