y
= 2x^2 + 3x - 2
= (2x^2 + 3x) - 2
= 2(x^2 + (3/2)x) - 2
= 2(x + (3/4))^2 - 9/8 - 2
= 2(x + (3/4))^2 - 25/8
Notice that 2(x + (3/4))^2 >= 0 for all real values of x.
Thus, maximum value is infinite and minimum value is -25/8.
domain is all real numbers, whereas range is [-25/8 , infinity)
As x tends to infinity, y also tends to infinity.
As x tends to negative infinity, y tends to infinity.
The interval of increase will be (-25/8 , infinity)
The interval of decrease will be (-infinity , -25/8)
How do we know this?
The answer is by looking at the end behaviour and the range.