Intermediate Algebra Find the Domain...?

1) y = 7x + 3

the domain is all the real numbers

2) y = (x - 2)/(2x^2 - 7x + 6)

y = (x - 2)/((x - 2)(2x - 3))

the domain is all the real numbers except x ≠ 3/2 , x ≠ 2

3) if it is:

y = ln_2(x - 5)

the domain is x > 5

and if it is:

y = log[2(x - 5)]

the domain is x > 5

4) y = 2^(x - 8)

the domain is all the real positive numbers: x > 0

5) y= 4x^2 - 2x + 3

the domain is all the real numbers

Edit: @ SynexRox : You are right about #4, I fixed my typo.

But for #2, the domain must be determined before removing holes i.e. by cancelling factors from denominator and numerator. Therefore the domain is all the real numbers except: x ≠ 3/2 , x ≠ 2

Slight modification to the above answer

2) y = (x - 2)/(2x^2 - 7x + 6)

y = (x - 2)/((x - 2)(2x - 3)) = ( 1 / (2x - 3))

the domain is all the real numbers except x ≠ 3/2

4) y = 2^(x - 8)

the domain is all the positive numbers

a million) The area is the set of numbers for which the the self reliant variable x is defined. The answere to #a million relies upon on the context. in case you're talking a pair of non-end function interior the airplane it relatively is the real numbers. in case you have been somewhat talking approximately discrete products the area may well be non-damaging integers or all integersif negatives are allowed. those are purely examples. 2) not sure what you advise. The slope is undefined everywhere? Vertical lines fulfill that.