4/13
- I. Review answers from test
- II. In text ch 3.1: polynomial, 3.2: continuous, discontinous
- III. Use the leading coefficeint and the degree of the polynomial to determine the
-
end behavior of the function.
-    
4/18
- I. Sketch using your knowledge of single roots, double roots,
- leading coefficient, degree of polynomial.
- See
dilation,
polynomials.
- 1. y = (x - 3)(x + 1)
- 2. y = (x - 3)²(x + 1)
- 3. y = (x - 3)²(x + 1)²
- Use your calculator to verify sketches.
- II. Divide x5 + x3 + x2 - 12x + 8 by x - 1
- see page 267 #1 then pg 283
4/20
- I. Evaluate y = x5 + x3 + x2 - 12x + 8
- when x is 1, -4, 2, -2
- Use calculators/synthetic division to verify answers.
- On 82 or 83, use table or
-     STO the x, then VARS then FUNCTION, then Y-VARS, then Y1, then ENTER
- On 85, use EVAL then the number, after storing function in the y(x) menu
-  
- II. Sketch
- 2. y = (x + 5)2(x2 + 4)2
- 3. y = (x + 5)3(x + 4)2(x - 3)2
- III. Solve
- 4. 0 = x4 - x2 - 20
- IV. The Division Algorithm - Use division to rewrite a function as the
- product of two factors plus a remainder.
- f(x) = (quotient function) · (divisor function) + (remainder function)
- If the remainder is 0, the divisor evenly divides the original function.
- IV. Consider examples of the above.
- ex 1. y = x2 + 4x + 4 = (x + 2)(x + 2) + 0
- ex 2. y = x2 + 4x + 5 = (x + 2)(x + 2) + 1
- ex 3. y = x2 + 6x + 4 = (x + 2)(x + 2) + 2x
- ex 4. y = 2x2 + 4x + 4 = (x + 2)(x + 2) + x²
- V. Text, pg 261. Sketch y = 3x4 - 4x3
- Find roots.
- y = 3x4 - 4x3 = 0
- x3(3x - 4) = 0
- x3 = 0 and 3x - 4 = 0
- x3 = 0 and 3x - 4 = 0
- x = 0 and x = 4/3
- 1st: Plot real roots.
- 2nd:Determine behavior of function about roots.
-     triple root at 0 -> passes through
-     single root at 4/3 -> passer through
- 3rd: Determine general shape & end behavior based on leading coefficient & degree of polynomial.
-     Quartic starts high, ends high.
From left to right, - graph decreases from positive infinity,
- still decreasing passes through x-axis at 0
- next increases and passes through
x-axis at x = 4/3 still increasing
- increases to positive infinity.
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