Determine if equations are functions; find domains; etc

[softball1145]

I need help on the following questions please:

1. Determine whether each of the equations are functions:

. . .a. x + 2y = 4

. . .b. x^2 + 5y^2 = 1

. . .c. x^2 + y - 7 = 0

2. Find the domain of each function:

. . .a. f(x) = 7x / (x-3)(x+4)

. . .b. f(x) = 2x - 10

3. Given the function f(x) = -2x^2 + 10x find the following:

. . .a. f(-1)

. . .b. all x-intercepts (if any)

. . .c. the y-intercept

4. Determine algebraically if the following functions are even, odd, or neither by finding f(-x).

. . .a. f(x) = 2x^4 + 5x^10 + 12

. . .b. f(x) = 3x^7 + 2x^5 + 10

. . .c. f(x) = -2x / x^4+1

Somebody please help me!!

 

[stapel]

1) If you can solve for a unique "y=", it's a function.

2) The domain is all allowable x-values. So look for any x-values that would cause problems (division by zero, a negative inside a square root, etc); the domain is everything else.

3) For part (a), plug in "-1" for "x". For part (b), plug zero in for y, and solve. For part (c), plug zero in for x, and solve.

4) Do the algebraic process they taught you: Plug "-x" in for "x", simplify, and then compare f(-x) to f(x).

If you are stuck, please reply showing how far you have gotten. Thank you.

Eliz.

 

[softball1145]

stuck

i haven't made much progress b/c im still not sure how to do it b/c i don't really understand math that well. so i would appreciate it if you might be able to help me out a little further please.

 

[softball1145]

question 3

for part a i have the following:
f(-1) = -2(-1)^2 + 10(-1) = -2 - 10 = -12

but for part be wouldn't you add zero to the x instead of the y in order to find the x-intercept.

 

[stapel]

i haven't made much progress b/c im still not sure how to do it...

Follow the links to learn "how to do it".

1) Solving Literal Equations and Functions

2) Domain and Range

3) Evaluating Functions and Finding Intercepts

4) Even and Odd Functions

The above lessons explain the concepts and give worked examples. Once you have studied and learned this material, please attempt the exercises. If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.