Lots of Pages Homework Pg. 184#41 – 53 all #28 C(7, 4) r = #33 #40 (-∞, -5/3]U[3, ∞)#42[-2, -1)U(-1, ∞) #52 (-∞, 2]#88y – axis #91 origin#104Does not pass.

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Lots of Pages Homework Pg. 184#41 – 53 all #28 C(7, 4) r = #33 #40 (-∞, -5/3]U[3, ∞)#42[-2, -1)U(-1, ∞) #52 (-∞, 2]#88y – axis #91 origin#104Does not pass HLT # 105 y = (x 2 /4) + 4 #106(- ∞, ∞) and [0, ∞) #107 a) origin; b) y – axis #15c = 17/3 #24 ↖ ↗#300.05x 7 #9 x = -3.60, -0.88, 1.63; max (-2.85, 74.12), (0.37, -2.52); min(-0.32, -3.43), (1.19, -4.33) #19 x = -5.81, 1.04, 6.27; max (-3, 211); min(4, -132) #24 D:(-∞, -5)U(-5, ∞); R:(-∞, 0)U(0, ∞); Discontinuous at x = -5 #26 D:(-∞, -0.5)U(-0.5, ∞); R:(-∞, ∞); Discontinuous at x = -0.5

3.1 Graphs of Polynomial Functions Information from a Function End behavior type End behavior model Determine domain and range Determine all zeros Determine y – intercept Determine all local min/max values Determine intervals of increasing/decreasing Draw a complete graph Find all the information for: When working with IVT, the function must be: ___________ Then you check: ____________ If the value is inside the endpoints, proceed to find the c. If the value is outside the endpoints, graph to know whether or not to proceed.

3.3 Real Zeros of Polynomials: The Factor Theorem Remainder Theorem If a polynomial is divided by x – c, then the remainder is f(c). Thus f(x) = (x – c)q(x) + f(c) where q(x) is the quotient. Examples Find the remainder when the polynomial: f(x) = x 3 + 3x 2 – 2x – 7 is divided by x – 2 x + 4

3.3 Real Zeros of Polynomials: The Factor Theorem Factor Theorem Let f(x) be a polynomial. Then x – c is a factor of f(x) if, and only if, c is a zero of f(x). -3 is a zero → x + 3 is a factor 5 is a zero → x – 5 is a factor Examples Use your calculator to find the zeros of: f(x) = 2x 3 – 4x 2 + x – 2 Use long division to prove x – 2 is a factor of f(x) = 2x 3 – 4x 2 + x – 2

3.4 Rational Zeros and Horner’s Algorithm Rational Zero’s Theorem If f(x) is a polynomial with all coefficients as integers and p as the constant term and q as the leading coefficient, then x = p/q is a rational zero. Examples Make a complete list of possible rational number zeros of f(x) = 12x 5 – 5x 3 + 4x – 15