I have some problems that I would like checked please.

Find and simplify the difference quotient f(x+h)-f(x)/h, h can not equal 0 for the given functions.

1. f(x)=x^2+3x+9- I got 2x+h+3

Evaluate the piecewise function at the given value of the independent variable.

2. g(x)={(x^2+2)/x-2 if x can not=2
{x+8 if x=2
Determine g(-5)

my options for the answer are: a. -5, b.3, c.3/7, and d. -27/7

-I got -27/7 and 3 when I solved it, but I don't understand what the question is wanting because -27/7 doesnt equal 2.

3. f(x)={-5x+4 if x<-3
{2x+3 if x > or equal to -3
Determine f(-7)

my answer options: a.39, b.-10, c.42, d.35

-I got 39 and -11 when I solved it and I also don't understand what the question is wanting.

What is 1/8(16m-8)+17 in simplest form

1. To find the difference quotient for the function f(x) = x^2 + 3x + 9, you need to substitute f(x + h) and f(x) into the difference quotient formula: (f(x + h) - f(x))/h. Let's calculate it step by step.

Substitute x + h into the function:
f(x + h) = (x + h)^2 + 3(x + h) + 9
= x^2 + 2hx + h^2 + 3x + 3h + 9

Substitute x into the function:
f(x) = x^2 + 3x + 9

Now, substitute these values into the difference quotient formula:
(f(x + h) - f(x))/h = [(x^2 + 2hx + h^2 + 3x + 3h + 9) - (x^2 + 3x + 9)]/h

Simplify the equation by eliminating like terms:
= (2hx + h^2 + 3h)/h

Now, factor out an h common to all terms:
= h(2x + h + 3)/h

Simplify by canceling out h:
= 2x + h + 3

Therefore, the simplified difference quotient for f(x) = x^2 + 3x + 9 is 2x + h + 3.

2. To evaluate the piecewise function g(x) at a given value, you need to substitute the given value into the appropriate part of the function based on the given conditions.

For g(x) = {(x^2 + 2)/(x - 2)} if x ≠ 2, and g(x) = x + 8 if x = 2.

To determine g(-5), substitute -5 into the first part of the function:
g(-5) = (-5^2 + 2)/(-5 - 2)
= (25 + 2)/(-7)
= 27/(-7)
= -27/7

Therefore, the value of g(-5) is -27/7.

3. To determine the value of the piecewise function f(x) at a given value, you need to substitute the given value into the appropriate part of the function based on the given conditions.

For f(x) = {-5x + 4} if x < -3, and f(x) = {2x + 3} if x ≥ -3.

To find f(-7), substitute -7 into the first part of the function:
f(-7) = -5(-7) + 4
= 35 + 4
= 39

Therefore, the value of f(-7) is 39.