By Lewis Parker Siceloff, George Wentworth and David Eugene Smith
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Y= 2 x - 2 x- 15 1. vVhen y = 0, then 4 x 2 - 12 x- 16 = 0, and x =- 1 or 4, the two intercepts. 1 -, they intercept. 2. The graph is not symmetric with respect to OX, 0 Y, or 0. 3. As to intervals, y is real for all real values of x. 4. As to asymptotes, the vertical ones are x =- 3 and x = 5; the horizontal one is y = 4, as was found in § 50. X vVe may now locate certain points suggested by the above discussion and draw the graph. 5, and 10. The two values of x near - 3 and the two near 5 enable us to notice the graph's approach to the vertical asymptotes, while the values- 8 and 10 suggest the approach to the horizontal asymptote.
V- (x 2 + G) (X - 2) . 46 LOCI AND THEIR EQUATIONS Examine each of tlte following equations with respect to intercepts and symmetry, solve for x in terms of y, determine the y intervals for which x is real or imaginary, assign values to y, and dmw the graph: 26. 3 X = 6 - 4 y2. 27. y2-x2 -4y=0. 28. (y- x)2 = 8y -16. 29. /)=y4 • 30. 3x2 + 2y 2- 2y=12. In Ex. 29 the point (0, 0) is called an isolated point of the graph. 32. A rectangle is inscribed in a circle of radius 12. If one side of the rectangle is 2 x, find the area A of the rectangle in terms of x, plot the graph of the equation in A and x, and estimate the value of x which gives the greatest value of A.
Xy-2y=x2 -;-16. 7. 3 x 2 - xy- 4 x + y = 7. 11. f -x 4 8. -4-= . 12. y 2 (5 10. + x)=- x 8• 13. y (3+x)=x (3-x). 2 2 14. f(x-4)-x2 (x-8)=0. 15. x 2(y+8)+y3 =0. 16. f. 17. 2 :J =9(x2-2x-8). ~-6x+5 18. y = ') x-4 2 """'x- 7 x- 4 19. A and Bare two centers of magnetic attraction 10 units apart, and P is any point of the line AB. P is attracted by the center A with a force P1 equal to 12/A P 2, 10 and by ~e center B with a force F 2 equal ~to 18jBP2• Letting x=AP, express in terms of x the sum s of the two forces, and draw a graph showing the variation of s for all v::Llues of ;::;, 52 LOCI AND THEil~ EQUATIONS 54.