Schaum's Outline of Theory and Problems of Beginning Calculus

22GRAPHS OF EQUATIONS[CHAP. 33.10On a single diagram, draw the graphs of:1 1y=x2 (b) y= 2x2 (c) y= 3x2 (d) y=jx2 (e) y=jx2Check your answers on a graphing calculator.3.1 1Draw the graph of y = (x - 1)2. (Include all points with x = -2, - 1, 0, 1, 2, 3, 4.) How is this graphrelated to the graph of y = x2? Check on a graphing calculator.1Draw the graph of y = -. Check on a graphing calculator.x-1Draw the graph of y = (x + 1)2. How is this graph related to that of y = x2? [H3 Check on a graphingcalculator.1.x+lDraw the graph of y = -Check on a graphing calculator.3.12Sketch the graphs of the following equations.x2y2(a) - + - = 1 (b) 4x2 + y2 = 44 9(4 Y =x3Check your answers on a graphing calculator.(c) x2 - y2 = 1[Hint: Parts (c) and (f) are hyperbolas. Obtain part (e) from part (a).]3.13Find an equation whose graph consists of all points P(x, y) whose distance from the point F(0, p)is equal to its distance PQ from the horizontal line y = -p(p is a fixed positive number). (SeeFig. 3-13.)0-p IFig. 3-133.14 Find the standard equations of the circles satisfying the given conditions: (a) center (4, 3), radius 1;(b) center (- 1, 9, radius fi; (c) center (0, 2), radius 4; (d) center (3, 3), radius 3fi; (e) center (4, - 1)and passing through (2, 3); (f) center (1,2) and passing through the origin.3.15 Identify the graphs of the following equations:(U) X’ + y2 - 12~+ 20y + 15 = 0 (b) x2 + y2 + 30y + 29 = 0(c) x2 + y2 + 3x - 2y + 4 = 0 (d) 2x2 + 2y2 - x = 0x2 + y2 + 2x - 2y + 2 = O (f) x2 + y2 + 6x + 4y = 36(e)