Consider the following points. (-1, 5), (0, 0), (1, 1), (4, 58) (a) Determine the polynomial function of least degree whose graph passes through the given points. p(x) = (b) Sketch the graph of the polynomial function, showing the given points. y y 1 2 4 -1 3 4 - 10 - 20 - 20 -30 -40 -40 - 60 - 50 - 60 - 80 y y 60 80 50 60 40 30 40 20 20 10 X 1 3 4 1 3 4 Need Help? Read It Watch It

Analyze the polynomial function f(x) = 4x (x²-9) (x + 5) using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph off behaves like y = for large values of x. (b) Find the x- and y-intercepts of the graph of the function. The x-intercept(s) is/are. (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) The y-intercept is (Simplify your answer. Type an integer or a fraction.) (c) Determine the real zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x-axis at each x-intercept. The zero(s) off is/are (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) Starting from least to greatest, the first zero of the function is of multiplicity, so the graph of f the x-axis at x =. The second zero of the function is of multiplicity, so the graph of…

The torque (in ft-lb)producedby a certainautomobileengine turning at x thousand revolutions per minute is shown in the table. Graph the points and then find a third-degree polynomial function to model the torque T(x) for lsxs 5. Engine speed (1000 гpm) Torque (ft-lb) 1.0 165 1.5 180 2.0 188 2.5 190 3.0 186 3.5 176 4.0 161 4.5 142 5.0 120

Draw (by hand) a graph of a polynomial function of degree 3 that has x-intercepts 1, 2, and 3, has a y-intercept of 6, and passes through the point (-1, 25). Can you actually have the graph you just drew?