6. Consider the circle centered at the point (-2, -1) whose diameter is 4. Draw this circle as accurately as possible, l

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6 Consider The Circle Centered At The Point 2 1 Whose Diameter Is 4 Draw This Circle As Accurately As Possible L 1 (61.11 KiB) Viewed 47 times

6. Consider the circle centered at the point (-2, -1) whose diameter is 4. Draw this circle as accurately as possible, labeling any points that are "nice". Let h= f(d) be the circular function that travels the circle counterclockwise starting at the rightmost point on the circle. Let d be the arc (distance), in radians, that you have traveled around the circle and let ħ be the height (y-value) of the coordinate point. a) Label the exact coordinates of 4 points on the circle. b) Find the corresponding points on the function h= f(d) (think carefully about the input and output). c) Sketch an accurate graph of h= f(d), labeling your axes as specifically as possible. d) State the midline, amplitude, and period of the function h. 7. Make sure to show how you got your answers or give some kind of justification for your answers. a) Consider the function g(t)=-42.5 sin (1.4(+2))-73.1. State the function's exact amplitude, midline, range, and period. b) For the function pictured below, determine a formula in the form p(t) = asin (k(t−b))+c or q(t) = acos (k(t-b))+c that fits the graph. Explain your thinking, referencing the function's amplitude, midline, and period, as well as any horizontal shifts you use. (3.6, 5) (0.6, 1) S. Make sure to show how you got your answers or give some kind of justification for your answers. a) Determine exact (ugly) values for a and b so that the exponential function m(t) = ab passes through the points (4, 15) and (8, 25). b) Draw an exponential function that is always decreasing and always concave up. Then find an equation that approximately fits your graph.