Advanced Algebra with Trigonometry: Quiz Ch 4 #1



left0006191250-10477500Advanced Functions and Modeling NAME ___________________Practice Quiz: 3.1 – 3.4 DATE __________ BLOCK ____ NON-CALCULATOR PORTION1) If P is a polynomial and a is a number for which , which of the following is true?a) is a factor of P. b) is an intercept of the graph of P. c) d) a is a zero of the polynomial.2) Divide by using synthetic division.3) Divide by using polynomial long division.4) Use this function and the synthetic division computations which follow. f(x) = x3 + 4x2 ? 47x ? 21037175931047750093345011430000 ?1 1 4 -47 -210B) 7 1 4 -47 -210 -1 -3 50 7 77 210 1 3 -50 -160 1 11 30 0 a) Can you determine a factor of f(x) from either computation? ______ If so, name it ______________b) Can you determine a root of f(x) from either computation? ______ If so, name it_______________c) What is f(?1)?__________ d) What is f(7)? __________e) What is the quotient when f(x) is divided by (x - 7)? __________________________4) Use the Remainder Theorem to find if . Demonstrate your work using synthetic substitution or polynomial long division. 5) At most, how many roots could the polynomial have?6) Determine the far-left and the far-right end behavior of the graph of As ____________As ____________ 7) Given the polynomial: Name the leading coefficient________, the constant_________, and the degree_________, the Cubic term __________, the quartic term __________, the quartic coefficient _______.Describe the end behavior. As ____________As ____________How many turning points are there? ___________IF we were solving, how many solutions? _____________Classify the following functions. Decide if the function is a polynomial function. If it is a polynomial function, state its degree, type, leading coefficient and general shape.8) f(x) = Polynomial?______Degree:______ L.C.:_______Type:______________9) Polynomial?______Degree:______ L.C.:_______Type:______________10) List all possible rational zeros of Possible Rational Zeros: _________________________________________________________________11) Find all zeros of. Use the Rational Zero Theorem to find your first zero. Zeros: _________________________________________________________________12) Answer the following and sketch the graph of . 372427542545List each real zero and its multiplicity:______________________________________________What is the degree of the polynomial? __________What is the maximum number of turning points? ________Describe the end behavior of the polynomial: As As 13) Find the x-intercepts of and state whether the graph of P crosses the x-axis or bounces at the zeros.48097914073300228600361950014)As x +, f(x) ____As x -, f(x) ____Relative maximum(s):_______Relative Minimum(s):_______Absolute Maximum:_________Absolute Minimum:_________348511154010015)11954215634300As x +, f(x) ____As x -, f(x) ____Real Zeros:______________Relative maximum(s):_______Relative Minimum(s):_______Absolute Maximum:_________Absolute Minimum:_________ ................
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