ALGEBRA 2 - DOMIAN and RANGE - HELP PLEASE - SIMPLE 4 U?

Question

Okay.. these are super simple but hard for me to concetrate at the same time .. please help..

What is the domain and range?

y = 25(-7x - 4)^(64)

y = (x^2)/(x^2-16)

y = 98(-6x - 5)^2

I think the answer for all of these is Domain = {all real numbers}, Range = {all real numbers}
Am I right... if not PLEASE explain

Answer 1

PROBLEM 1:

Domain is all real numbers (because you can put anything in for x without restriction).

However, think about the values of something to the 64th power. This is an even power, so it will always be positive. And multiplying by 25 won't change this.

So the range is all non-negative real numbers (y ≥ 0)

PROBLEM 2:

Here you have a denominator. Remember you can't ever divide by zero. So you can't have (x² - 16) being zero. That eliminates x = 4 and x = -4.

The domain is all real numbers except x = 4 and x = -4

For the range, think of this as:
...... x²
----------------
(x - 4)(x + 4)

The numerator will always be positive. For x > 4, the denominator will be positive. For x < 4, the denominator will also be positive. For x = 0, the you'll get 0. For -4 < x < 4, you'll get the denominator being negative (one term positive, one term negative).

That pretty much covers all real numbers, so the range is all real numbers.

PROBLEM 3:

Same logic as PROBLEM 1...

Answer 2

1. The domain is all real numbers but the range is all positive real numbers (and 0) because the exponent 64 is an even number, therefore the answer will always be positive (or zero when x = -4/7

2. What happens when x = 4 and x = -4?
x^2 - 16 = 0 and you can't divide by 0, right? So, x cannot be in the domain but every other number can be in the domain.
The range is every real number

3. The same type of argument applies to this one, as to 1.

.

Answer 3

Subtracting 4 from the two sides you will get 3x^2-x-4=4-4 3x^2-x-4=0 Now factorizing you will get 3x^2-4x+3x-4=0 taking away ordinary you will get x(3x-4)+a million(3x-4)=0 (x+a million)(3x-4)= 0 the two x+a million = 0 or 3x-4 = 0 x = -a million or 3x=4 x= -a million or x= 4/3 --- answer great AnswerNot HelpfulReport