Lesson # 1: Functions You Should Know

1) Linear   y = mx+ b   (m = slope, b = y-int)                             

Example: y = 1/2x+2
    rise = +1
    run = +2                                                             
    y-int = +2

                                                                                      

2) Quadratic   y = (x+2)^2 -1                                                    Parabola = *root* (-2,-1)
                             

3) Cubics   *Deg 3* 

          

 y = (x+2)(x-3)(x-4)                                  Leading Term = x^3....+24

 zeros =-2, +3, +4

 y = -(x+1)^2(x-2)                                    Leading Term = -x^3....+2
 zeros =-1, -1, +2

*The negative makes it flip vertically*

4) Quartics   *Deg 4*                                        

                         
y = (x+1)^2 (x-2)(x-3)                                    Leading Term = x^4....+6

                        

5) Reciprocal   y = x  >> y = 1/x                      

a) draw base

b) vertical asymptote (zeros)

c) imvarient

d) reciprocal heights

                                                        

                                                       

6) Circles   r = 2                                              

 x^2+y^2 = 4

             y = 4- x^2

             y = *root*(4- x^2)       *top half*

             y = -*root*(4- x^2)     *bottem half*

                                                      

                                                         

7) Absolute Value   y = |x|                                                                         



|5| = 5

|0| = 0

|-2| = 2                                    

                                                    

8) Sqaure Root   y = *root* (x)        

             

 X   Y

 0    0

 1    1

 4    2

 9    3

-4   n/a            

                                              

9) Exponential   y = 2x

           

 X   Y

 0    1

 1    2

 2    4

 4    8 

-1  1/2

-2  1/4