100 points help or reported.

Check the explanation for each thoroughly.

Step-by-step explanation:

So sorry for the wait !

1. a) f(x) = 9/(x-10) + 21                                            

Set the denominator to 0, and solve for x:

x - 10 = 0, x = 10

   b) Bring on common denominator, and check the degree:

       9/(x-10) + 21 = 21x - 201/x - 10,

       horizontal asymptote => 21/1 = 21, y = 21

2. The removable discontinuity will occur at an undefined point, which will be when the denominator = 0:

x + 4 = 0, x = -4

3. Remember that the domain is a set of input for which the function is real. The value under the square root respectively should be ≥ 0 -- to be defined:

x + 16 ≥ 0,  Doman: x ≥ - 16

And the range is the set of values of the dependent variable for which the function is real, defined:

Range: f(x) ≥ 7

4. a) The parabola opens upward because the coefficient is positive [+3}

   b) Evaluate the x-value of the vertex of the parabola:

       x = -b/2a = -(-12)/2*3 = 2

       line of symmetry: x = 2

   c) Since we already have the x-value of the vertex, plug this in the

       equation and solve for y:

       y = 3(2)^2 - 12(2) + 7 = -5

       Vertex: (2, -5)

5. Equation: f(x) = -0.536x^2 + 9.03x + 5.43

6. The graph is shifted 8 units down, and 3 units to the right respectively

7. Check the attachment below

8. I believe this is your equation...?:

If so, then the point of maximum growth would be 600. This is self explanatory, because the horizontal asymptote = 600.