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Randall Barnes
(a) The polynomial function f is given by State the potential rational zeros of QUOTE . Describe the end behaviour of QUOTE and state the maximum number of turning points that the graph of QUOTE could have. Show that x + 5 QUOTE is a factor of QUOTE Derive all the zeros of QUOTE , state their respective multiplicities and whether they touch or cross the x axis. (b) Three zeros of a polynomial function QUOTE of degree four are 4, -1-2i and -7i. Determine the polynomial f (c) Use appropriate transformations to sketch the graph of QUOTE 2) (a) Sketch the graph of the function given by . Identify all asymptotes and intercepts if they exist. Also state the domain and range of the function. (b) Find all real solutions to the following equations (i) (ii) 3. (a) The perimeter of a rectangle is 22 inches and its area is 24 square inches. (i) Find two equations that describe the information given above. (ii) Using the method of elimination find the two numbers. b) Write the partial fraction decomposition of the following rational functions: i) ii) 4. (a) A rational function is given by Find the domain of the function. Identify all asymptotes, and intercepts of the graph of f. (c) Solve the following inequality QUOTE (d) Determine whether or not the following function has a zero in the following interval: QUOTE 5. (a) Determine the centre and radius of the circle given by the equation below QUOTE (b) Find the equation of the parabola with vertex at (0,0) and focus at (-2,0). Graph the equation. (i) Find an equation of the parabola with vertex at (4,3) and focus at (0,3) (ii) Graph the equation of the parabola (d) A bridge is to be built in the shape of a parabolic arch and is to...
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