iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii
' Name: Section: ID #: Show appropriate work on all problems below. Place answers in the blanks provided. Give exact answers and simplify your answers to all problems if possible, 1. (10 pts) The polynomial, P, of degree 5, has zeros of multiplicity 2 at x = 5 and x = 4, and a zero of multiplicity 1 at x = 0, and it passes through the points (2, 7). Find a possible formula for P(x). (Write your answer in function notation and in a factor form) 2. (15 pts) Answer the following of the polynomial and then graph the function. f(x) = -2(x - 3)2(x - D305 + 2) Degree of f3 End behavior: IIII IIII IIII Test points: y-intercept (as a point): 3. (10 pts) Find a possible formula r for the following function. (Write your answer in function notation and in a factor form) 4. (10 pts) A box with a square base and no top is to be made from a square piece of cardboard by cutting 3 in. squares from each corner and folding up the sides. The box is to hold 363 in3. Let x be the length of the cardboard. Write the volume, v, of the box in term of the length. Also, how big a piece of cardboard is needed? Function: Length: Width: x3 - 8 x2 + 5x + 6 ' a. Does the rational function have the horizontal or oblique asymptote? 4. (10 pts) Suppose r(x) = b. Find the asymptote. in part (a): c. Find the vertical asymptotes: i. (20 pts) 0f the rational function, nd the domain, all the x- and y- intercepts; the horizontal asymptotes; the intersection between the function and the horizontal asymptotes ,if any; the vertical asymptotes; the behavior near by the vertical asymptotes; and obtain the graph of r. ( )_ 2x2 8 y r x x2 + x 12 Factor: Domain: x-intercepts: {I x y-intercepts: V.A: Behavior nearby the VA: H.A: Find the intersection between the graph and H.A: \\ 7. (15 pts) Let f (x) = x2 + 6x. Find the vertex, minimum or maximum value, x- and y- intercepts, and graph f (x). \\ The Vertex is: The minimum or maximum value is: The Axis of symmetry: Vertical intercept (as a point): Horizontal intercept(s) (as point(s)): ' Vertex form: 8. Find the domain of the function. (Write your answer in interval notation) f (x)= x/(x+2)2 (x '5) (Bonus 1 pts each) consider the function f (x) = 4x3 + 5x6 x9 and answer the following: a.) What is the degree of this polynomial? b.) What is the leading coefcient in this expression? c.) What is an? d.) What is as? e.) Write the polynomial in Standard Form: f.) At most, how many turning points does the mction have? g.) At most, how many xintercepts does the function have? 11.) At most, how many y-intercepts does the function have? i.) Asx-> 0, f(x) ' _? j.) Asx-> -, f(x) -* _
