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1.)given the polynomial: f(x)= -2(x+2)(x-3)(x-1)2 a.) the graph of the function will resemble what power function? ___cubic power function __ b.) choose the correct representation of the endpoints of the function. _____ b ______ c.) find the y-intercept(s). write as ordered pair(s). _________(0, 12).______________ f(x) = -2(x+2)(x-3)(x-1)^2 f(0) = -2(0+2)(0-3)(0-1)^2 f(0) = -2(2)(-3)(1)^2 f(0) = 12 therefore, the y-intercept is (0, 12). d.) list the real zeros, their multiplicity, and whether the graph will cross or touch the x-axis at the zero. use as many blanks as needed. you may not need them all. real zero multiplicity cross or touch -2 1 cross 3 1 cross 1 2 touch e.) what is the maximum number of turning points? ______2_______ f.) using a graphing calculator or desmos to find the following. if you are using a graphing calculator, adjust your window to: xmin = -5, xmax = 5, ymin = -10, ymax=35. a. calculate the turning point(s); round to one decimal place. write as ordered pair(s). ___(-2.0, 24.0) and (3.0, -27.0)______ b. where is the function increasing and/or decreasing? use interval notation. round to one decimal place. • increasing: _____(-∞, -2) u (1, 3)___ • decreasing: ____ (-2, 1) u (3, ∞)___ g.) what is the domain? (use interval notation.) ____(-∞, ∞) __ h.) what is the range? (use interval notation.) ___ ((-∞, 12) ___ analyze the function (𝑥) = 𝑥 4 − 4𝑥 3 − 7𝑥 2 + 36𝑥 − 18. <ol>domain: __r __ or__ (-∞, ∞) ___ </ol> ii. leading power function that the graph resembles for large values of |x| (𝑥) = ___x4__ iii. choose the correct representation of the endpoints of the function. __a______ iv. possible rational roots: <ol> p = factors of -18 = ±1, ±2, ±3, ±6, ±9, ±18 q = factors of 1 = ±1 p/q = ±1, ±2, ±3, ±6, ±9, ±18 </ol> v.find the roots: root factor cross or touch or imaginary? -3 x + 3 cross +3 x – 3 cross 2 - √2 x – 2 + √2 cross 2 + √2 x – 2 - √2 cross vi. factored form: (𝑥) = (x + 3)(x - 3)( x2 - 4x + 2) = (x + 3)(x - 3)(x – 2 + √2)(x – 2 - √2) 3.) suppose a function had the following end behavior. answer the following questions. a. would the leading coefficient be positive or negative? ___negative_____ b. would the degree be even or odd? __even____ 4.) suppose a function had the following end behavior. answer the following question. a. would the leading coefficient be positive or negative?__negative__ b. would the degree be even or odd? __odd_______ 5.) use the graph to answer the questions below. a. based on the graph above, does the x-intercept of -2 have even or odd multiplicity? ___even___ b. based on the graph above, does the x-intercept of 1 have even or odd multiplicity? ____odd__ c. based on the graph above, does the x-intercept of 0 have even or odd multiplicity? __even___ d. would the leading coefficient be positive or negative? ___positive_______ e. what is the minimum degree for the polynomial above? ___4____