Question

6. Given x2 + y2 - 4x -Ny-16 = 0 is the equation of a circle in general form, which of the following represents the standard form of this circle? A) (x-4)2 + (y - 3)2 = 36 B) (x - 2)2 + (y - 4)2 = 36 6) C) (x - 2)2 + (y - 4)2 = 6 D) (x + 4)2 + ( + 8)2 = 36 E) None of the Above 7. Write the equation of a function, such that y is a function of x, that is finally graphed after the following transformations have been applied to the graph of y = Vx. (1) Shifted Right 3 units. (2) Shifted up 6 units. A) y = x - 3+ 6 B) y = (x + 6-3 7) C) y = x +3+6 D) y= x – 3 – 6 E) None of the Above 8. Determine whether the given quadratic function has a maximum or a minimum value and find the value: f(x) = -3x2 + 18x A) Minimum Value of 27 at x = 3 B) Minimum Value of 3 at x = 27 8) C Maximum Value of 27 at x = 3 D) Maximum Value of 3 at x = 27 E) None of the Above 9) 9. Identify the degree of the following polynomial function: f(x) = 9x(x - 2)²(x + 3)* A) Degree of 4 B) Degree of 6 C) Degree of 8 D) Degree of 7 E) None of the Above 10. Which of the following is a true statement about the following function: x244 A) The graph of f(x) has a Horizontal asymptote at y = 0 B) The graph of f(x) has an Oblique asymptote at y = x + 4 C) The graph of f(x) has a Horizontal asymptote at y = 2 D) The graph of f(x) has a Vertical asymptote at x = 2 E) None of the Above 10)

Answer 1

y (6) x? + y2 - 4% -84 -16 = 0 (x2-4 x +4) + (y2-8y + 16 ) - 2076=0 (x-2)2 + (y-4)? - 36 Equation of in de =) (x-2) + (-4) = 36 Option B is corrut (7) (1) Shifted Right 3 units i, 9 5X-3 & (2) Shifted 6 ath units up y = 5 X -3 + 6 Equation of Function => y = 5X-3 + 6 option A

Degree of 4 f(x) & f'(x) (8) - 3x² +18x -6% + 18 Y 3 & f'(X) = -6 has rive pifitate maximum valu at i function X-3 i e f(3) -3(3%) + (18*3) U lill = 27 27 +54 maximum value 27 at * = 3 (9) f(x) 9 x (x-2)? (x+3) 4 degree 1+ 2+4) = 7 (0)

= (10) f(x) 2x +3 X? +4 Since denominator can not be zero therefor vertical arrymptates does not exists ¢ as x D Lim 2x+3 - Lim X? +4 ХЭop 27 31% Xtoo x +41x Tim f(x) ХЭД 0 yao in Horizontal assymptates