Functions, Equations, Graphs PDF

Functions SED18 1. 4 , Equations Graphs Polynomial functions have whole number exponents a of in the form an" + but car constantterm + +...

Functions SED18 1. 4 , Equations Graphs Polynomial functions have whole number exponents a of in the form an" + but car constantterm + +.. -- P(x) 3x" + 52-1 is eg =. a polynomial foo = 3x7 + 4x - g - - isNot polynomial a We can graph polynomial functions with a table of values (this is method that a we have used before to help We will use intercepts us sketch our function & -x-intercepts (2 0 where 0 y = , y = PG) = 0 we need to factor the polynomial to find the xe intercepts (Pcal = 0)  Consider PG = 2 - Ex + 6 possible E [1 , 2 , 3 , 63 p( = 1 - 7+ 6 = or = (2-1) is a factor I Q+ - 6 = (x + 3)(x - 2) (2 + 3) (x-2) PGQ (Ll) O = = d ↓ x = 1 x= =2 x These are the x-intercepts 2) Hintercept (0 , y) zo y = 6 the constant term ! Points (1 0) (3 , 0 (2 , 0) (0 , 6) , pos cubic -. Q3 - Q1 3 parts In this case , each root has a multiplicity of. 1 Root = zero = -intercept Consider feel : - ** Get This is a positive ! d ↓ quintic Intercepts : n =4 x = - 1 4 (1) 2 y-interupt : f(0) = 1 - = - 64 t Q3 - Q1 ~ much of 3 came from this actually 3 brackets NOTE : ODD multiplicity root goes the through EVEN multiplicity does Not g o through the root  PGOT (a + (1 1) G2+ 2) Try = - : as find the intercepts wat : x= -1 , 1 , -2 yust : y = (1) ( 1) (2)- = =2 Sketch the and describe the function b) graph multiplicity of * so go the 2 do through root NOT positive quartie Q2eQ  fixt -x + 3x2 TRY +x 3 = - [51 33 possible , P() = -1 + 3 + -3 v > - G-1) is a factor 3 (13) - - 1 Q : + 2x + 3 = - (x2 - 2x 3) - - - (n+ 1)( 3) - P(u) (x 1) (x+ 1) ( 3) - i - = - - ↓ E ↓ multiplicity 3 ↓ x= 1 x= 1 = 3 is I y-it : -3 neg. cubic Q2 Q4 y = * - HN