Need help w/ functions: diff. quotients, evaluation, etc

[MissAmy7]

I am really REALLY bad with mathematics and I am struggling to understand these practice problems. Below are the problems I cannot grassp. Please someone help me! I will be forever grateful!!

Here are the terrifying problems:

1. Find and simplify the difference quotient for f(x) = 2x + 7

Note: The "difference quotient" is [f(x + h) - f(x)] / h, h not equal to 0.

2. Find and simplify the difference quotient for f(x) = 3x^2

3. For the function f(x) = 2x^4 - x^2 + 1, evaluate f(-x)

(this one gives choices, but it does not help me out)
A. f(-x) = x^4 -x^2 + 1
B. f(-x) = 2x^4 -x^2 + 1
C. f(-x)= 2x^4 + x^2 + 1
D. f(-x) = 2x^4 -x^2 - 1

4. Evaluate the piecewise function:

. . . . . . . . ./ 9x for x < 0
. . .f(x) =<
. . . . . . . . .\ 3x - 3 for x > 0

(this one gives choices too, but again does not help me)
A. f(-3) = -9
B. f(-3) = 27
C. f(-3) = -27
D. f(-3) = 9

5. Find the domain of the functiion f(x) = 3 /(x - 3)

A. domain = (-oo, -3) or (3, oo)
B. domain = (-oo, 3] or [3, oo)
C. domain = (-oo, -3] or [3, oo)
D. domain = (-oo, 3) or (3, oo)

6. Identify whether the function f(x) = 2x^2 - x is even, odd, or neither.

7. Identify whether the function f(x) = x^2 - x and g(x) = x + 5, find
(g o f)(x).

A. x^2 + x + 5
B. x^2 - x + 3
C. x^2 - 2x + 5
D. x^2 - x + 5

8. Identify whether the function f(x) = x^2 - x^6 is even, odd, or neither.

Thanks ahead of time!!!!!!!

Amy

 

[stapel]

1) Plug "x + h" in for "x". Simplify to find f(x + h). Subtract f(x) from f(x + h). Simplify to find the numerator. Divide the result by h. If possible, factor an h out of the numerator, and cancel.

2) This one works just like (1).

3) Plug "-x" in for "x". Simplify.

4) I will guess that the instructions specify somewhere to evaluate the function at x = -3...? If so, pick the rule that applies for x = -3, and plug -3 in for x. Simplify to get the answer.

5) The domain is all allowable x-values. Are there any x-values which would cause a square root to contain a negative? A logarithm to contain a non-positive? A denominator to contain a zero? Etc. The domain will be all other x-values.

6) Follow the algorithm they gave you: Plug "-x" in for "x", and compare the results with the original function. If f(-x) is exactly the same as f(x), then the function is even. If f(-x) has all signs opposite to f(x), then the function is odd. If neither, then the function is neither.

7) I will guess that the instructions are to find the composition, not to determine or "identify" something...? If so, then convert "(g o f)(x)" into the more intuitive "(g(f(x))". Then plug f(x) in for "x" in the formula for g(x), and simplify.

8) This one works just like (6).

If you get stuck, please either specify that you need links to lessons so that you can learn the necessary background material, or else show how far you have gotten in applying the relevant formulas and such. Thank you.

Eliz.