Function and limits

What is the sin cos identity

What is the sec tan identity

What is the cot cosec identity

What are all the addition identity (sin, cos and tan)

What is the subtraction identity (sin, cos and tan)

What is the product identity (sin, cos and tan)

What is the double angle identity (sin and cos)

What is the half angle identity (cos and sin)

What are the 4 ways a function can be expressed as?

• Verbally

• Visually (Graphically)

• Numerically (Table)

• Algebraically

What is a function?

Function, f , is a rule that assign to each element x in a set D (domain) exactly one element, called f(x), in a set E (Codomain)

What is the convention for domain (D) and codomain (E)

E∈R and we take the largest possible set to for which the rule makes sense (D → largest possible is R)

What is the range of a function defined as?

The range of f is the set of all possible values of f(x) as x varies throughout the domain

How do you express f (function) and connect it to the domain (D) and the codomain (E)

Note: f, D and E are just placeholder

What is the difference between the codomain and the range?

• Codomain: What may possibly come out of a function

• Range: What actually comes out of a function

(Like every possible value on the y-axis is the codomain while the actual outputs is the range)

What is a vertical line test?

What is the first step to make an equation a function?

If it is comprised of more than 1 function, limit the functions you don’t want

What is the difference quotient

What is a piece-wise function

A function where more than one formula is used to define the output over different pieces of the domain (Kinda like lego)

What is the definition of an absolute value function?

Draw the mother graph of an absolute value function

What are the properties of the absolute value

How to use sign table ?

The critical values are where the absolute function is changing their sign and where you get 0 or undefined (fractions)

What are the properties of an even function?

It is reflective over the y-axis

What are the properties of an odd function?

How to check if a function / expression is reflective over the x-axis?

Sub y as -y and see if you get back to the original function

How to check if a function is reflective over the y = x line?

Sub x = y and y = x and check if you get back to the original function

What is the definition of an increasing function?

What is the definition of a decreasing function?

What is a mathematical model?

What is the general linear formula?

What is the general polynomial function formula?

What is a shape of a graph if the degree of the polynomial is 0

What is a shape of a graph if the degree of the polynomial is 1

What is a shape of a graph if the degree of the polynomial is even (>=2)

What is a shape of a graph if the degree of the polynomial is odd (>2)

What is the general formula for power function?

What is the general shape of a power function where n is a positive integer

2 → for every even integer >=2

3 → for every odd integer >=3

What is the general shape of a power function where n is a negative integer

-2 → for every even integer <= -2

-1 → for every odd integer <= -1

What is the general shape of a power function where n is a fraction

What is the general formula for a rational function

Steps when dealing with rational function

What are rules with inequality

What is the definition of a periodic function?

Express tan x using sin x and/or cos x

Express cot x using sin x and/or cos x

1/tanx

Express cosec x using sin x and/or cos x

Express sec x using sin x and/or cos x

Draw the function sin x

What are the property of sin x

Draw the cos x graph

What are the property of cos x graph

Draw the tan x graph

What are the property of tan x graph

Draw the cot x graph

What are the property of cot x graph

Draw the cosec x graph

What are the property of cosec x graph

Draw the sec x graph

What are the property of sec x graph

What is the law of sines?

What is the law of cosine?

What is the formula to get the area of any triang

What is the definition of exponential function?

What are the 3 different possible shape of an exponential function if the b values ranges from 0 (exclusive) to +infinity

What are the laws of exponent

What are composite function

What is so special about Euler’s number

How to decompose functions

Think of the mother function and how I manipulated it

What do you do in order to transform a function to horizontally or vertically shift it

What do you do in order to transform a function to stretch or reflect it

What is an inverse function

How to proof a function is one-to-one

Try to proof by contradiction

What test can you do on the original function to check if the inverse function is a one-to-one function

What are the property with inverse function and the original function (cancellation)

How to find the inverse of a function

What is the derivative of an inverse function

What are the properties of log

What are parametric equations

What are the steps to get the general shape of a parametric function?

What is a parabola?

What are the possible parabola shapes

How to shift parabolas?

What are the general formula for parabola?

What is an ellipses?

On a ellipses, what is the sum of the distance from two focii to same (any) point on the circumference

What are the x-int, y-int, focii points and general formula for ellipses where it is more pulled in the x direction

What are the x-int, y-int, focii points and general formula for ellipses where it is more pulled in the y direction

What is a hyperbola

On a hyperbola, what is the difference of the distance from two focii to same (any) point on the circumference

Give a summary for hyperbola

Give a summary for ellipses

Give summary for parabola

What is the condition for an ellipse to be a circle?

Where c = 0 → a = b