1. 
y = 2x + 5 It is possible to replace x
with any real number and get a value of y.
Since we double every value of x and then
add 5 to it, we can do this for any value of
x. It is also possible to generate any value for y
by selecting appropriate x values.
Therefore: 

Domain: all real numbers 

Range: all real numbers 

2. 
y = x^{2}  4 It is possible to replace x
with any real number and get a value of y.
However since x^{2} is never
negative, x^{2}  4 is never less
than  4 so the range will be all real
numbers greater than or equal to  4.
Therefore: 

Domain: all real numbers 

Range: all real numbers such that y > 
4 

3. 
y = The square root is real if the quantity under the
square root is greater than or equal to zero.
We need x  5 > 0 or x > 5.
The range cannot be negative so y will be any real number greater
than or equal to zero.
Therefore: 

Domain: all real numbers such that x > 5 

Range: all real numbers such that y > 0 

4. 
y = The denominator cannot equal zero so if we set the
denominator equal to zero we will find the values which are excluded from the domain.
x  3 = 0
x = 3
So the domain is all real numbers except x
= 3. The range will take on all real numbers except y = 0 because no matter what you plug in for x in the equation, the value of y will never be zero.
Therefore: 

Domain: all real numbers, such that x cannot equal 3 

Range: all real numbers, such that y cannot equal 0 
