Please enable JavaScript.

Coggle requires JavaScript to display documents.

Unit 2 - Coggle Diagram

- - - - Radical
        
        a negative inside of a radical
        
        Property
        
        -M =-1*M=iM
    - - the cycle of i repeats every 4th power
      - i,-1,-i,1
    - - written in the form a+bi
      - b is the imaginary part
      - Adding complex numbers
        
        combine like terms
- - - - x^2-Y^2
      - Factored as (x-y)(x+y)
  - - - used to determine the nature of a solution to a quadratic expression
      - b^2-4ac
      - d is greater than 0 then there are 2 solutions
      - d less than 0 there are 2 non-real solutions
      - d Is equal to 0 then there is one solution
- - - - read the problem
      - create a equation
      - solve using Pythagorean theorem
- - - - substituting the value of f(x) into the equation to solve
      - Root function
        
        f(x)=ng(x) is a root function
        
        n is an integer that is greater than or equal to 2
        
        Domain of a function
        
        y=f(x) is the set of all x
  - - - substituting f(x) for y to solve an equation
    - - f(x+h)-f(x)x-+h-x=f(x+h)-f(x)h
    - - a function of the term f(x)=g(x)h(x),
      - g(x) can't equal zero
      - h(x) is greater than xero
- - - - can have an infinite number
      - when y is equal to zero
      - f(x)=0
      - Intercept function
        
        used to find the intercept of a function when not given a graph
        
        Substitute x for zero in a n equation to find the y intercept
        
        substitute y for zero to find the x intercept
        
        Determine the function
        
        Rises for left to right- Increasing
        
        Falls from left to right- decreaseing
        
        the graph is horizontal- constant
        
        Relative maximum
        
        tallest point on the graph
        
        Relative Minimum
        
        Lowest point on the graph
        
        Even function
        
        when a graph contained the negative reciprocal of the domain
        
        f(-x)=f(x)
        
        Odd function
        
        2 more items...
- - - - gives each number in the domain the squares of that number in the range
      - f(x)-x^2
      - Cube function
        
        gives each number in the domain the cube of that number in the range
        
        f(x)=x^3
        
        Absolute value function
        
        gives each number in the domain the absolute value of that number in the range
        
        f(x)=IxI
        
        Square root function
        
        gives each number in the domain the squares root of that number in the range
        
        all x's greater than of equal to zero
        
        f(x)=square root of x
        
        Cube root function
        
        give all numbers in the domain the cube root of that number in the range
        
        Reciprocal function
        
        gives each number in the domain its reciprocal in the range
        
        has two asymptotes
        
        Sketching functions with restricted domains
        
        3 more items...
- - - - shifting the graph horizontally left or right
      - Reflection about the x-axis
        
        from y=f(-x) to y=f(x)
        
        Reflection over the y-axis
        
        from y=f(-x) to y=f(x)
        
        Vertical strech
        
        a greater than 1
        
        af(x)
        
        vertical compression
        
        0 is less than a and a is less than 1
        
        Horizontal compression
        
        a greater than 1
        
        f(ax)
        
        Horroziontal strech
        
        2 more items...