fx 4x 8 g gx 9x 7 Find gx A 13x2 100 15 B 36x2 79x 5

f(x) = 4x + 8, g g(x) = 9x + 7 Find (g)(x). A) 13x^2 + 100 + 15 B) 36x^2 + 79x = 56 C) 36x^2 + 56 D) 36x^2 - 100x + 56 Give the equations of any vertical asymptotes. F(x) = x - 7/x^2 + 2x A) x = 2 B) x = 7 C) x = -2 D) X - 0, x = -2 Give the equation of any horizontal asympletes. g(x) = x^2 + 8x - 3/x - 3 A) y = 8 B) y = -3 C) y = 0 D) none Provide an appropriate response. For what value of c does the quadratic function f(x) = 3x^2 + 8x + c have exactly one x -integral? A) - 2/3 B) 16 C) 16/3 D) 2/3 Solve the inequality, write the solution set in integral motation. 2x^2 - 9x Greaterthanorequalto 18 A) (-x, -6) u [3/2, x] B) [- 3/2, 6] C) [-x, - 3/2] u [6, x) D) [-6, 3/2] 3x^2 + 2x

Solution

15) (fg)(x) = f(x)g(x) = (4x+8)(9x+7) = 36x²+28x+72x+56 = 36x²+100x+56...Option D is correct

16) Equation of vertical asymptotes is given by:

x² + 2x = 0 => x(x+2) = 0 => x=0 and x=-2...Option D is correct

17) As degree of numerator is greater than degree of denominator so no horizontal asymptote..Option D is correct

18) For x-intercept, f(x) = 0

=> 3x²+8x+c = 0 ..This is a quadratic equation and it has exactly one root only if D = b²-4ac = 0

That is D = (8)²-4(3)(c) = 0 => 64-12c = 0 => c = 64/12 = 16/3...Option C is correct

19) 2x²-9x> = 18

Consider 2x²-9x-18 = 0 => 2x²-12x+3x-18 = 0 => 2x(x-6)+3(x-6) = 0 => (2x+3)(x-6) = 0

Hence we get x=-3/2, 6

Now for (-infinity, -3/2)..let x=-2 then 2(-2)²-9(-2)-18 = 8+18-18 = 8>=0 Hence (-infinity, -3/2] is in the solution

For (-3/2,6) ..let x=0 then 2(0)-9(0)-18 = -18<0 hence (-3/2,6) is not in solution

For (6,infinity)..let x=7 then 2(49)-9(7)-18 > 0 hence [6,infinity) is in soltuion

So the solution is given by: (-oo,-3/2] U [6,oo)...Option C is correct

20) 3x² + 7x<20

Consider 3x²+7x-20 = 0 => 3x²+12x-5x-20 = 0 => 3x(x+4)-5(x+4) = 0 => x=-4, 5/3

So For (-infinity, -4) ..let x = -5, 3(25)+7(-5)-20 = 75-35-20>0 Hence (-infinity,-4) is not in solution

For (-4,5/3)...let x=0, 3(0)+7(0)-20 <0 Hence (-4,5/3) is in soltuion

(3,infinity)..let x=4, 3(16)+7(4)-20 = 48+28-20>0 Hence (3,infinity) is not in solution

The solution is given by (-4,5/3)..Option B is correct

21) M(x) = 16x-x² = -(x²-16x) = -(x²-16x+64-64) = -(x-8)²+64

This represent downward parabola with vertex (8, 64)

Hence x coordinate 8 in rainfall gives maximum number that is 64 mosquitoes...Option D is correct