As it is always the case that correct answers without sufficient mathematical justification may not receive full credit, make sure that you show all your work. Please circle, draw a box around, highlight, or otherwise clearly indicate your final answer for each question. By signing your name above, you attest to the fact that the work you are presenting is wholly your own. Attach all work to this coversheet. Give both the standard form and the general form of the equation of the circle with... a) a radius of 4 centered at the point (2, -3). b) endpoints of a diameter at (4, 3) and (0, 1). Give the center and radius of the circle defined by the equation x^2 + y^2 + 4x + 2y - 20 = 0. Graph the circle. Suppose f (x) = -2x^2 + x - 1. Find each of the following values. a) f (0) b) f (1) c) f (-1) d) f (-x) e) -f (x) f) f (x + 1) g) f (2x) h) f (x + h) Find the domain of each of the following functions. a) f (x) = x + 4/x^3 - 4x b) f (x) = Squareroot -x - 2 Let f (x) = Squareroot x + 1 and g (x) = z/x. Find a formula for and the domain of the sum, difference, product, and quotient of these functions. lf f (x) = 2x - 8/3x + 4 and f (2) = 1/2, what is the value of B? Express the area A of a rectangle as a function of the length x if the length of the rectangle is twice its width. Use the graph of the function f, given to the right, to answer the following questions. a) Find f (0) and f (6). b) Find f (2) and f (-2). c) For what values of x is f (x) = 0? d) For what value of x does f (x) = 3? e) For what value of x does f (x) = -2? f) Is f (3) positive or negative? g) It f (-1) positive or negative? h) For what values of x is f (x)
