How do you find the domain and range of #y=2x^2  4x  5#?
1 Answer
Apr 3, 2018
Ask yourself where the function is defined.
Explanation:
In your case the domain is the whole real ax
Other examples:
 logarithmic functions:
#f(x)=log(x)#
logarithmic functions are not defined for non positive argument so check where the argument is#<=0# .
The range is

exponential functions:
#f(x)=e^x#
The domain is#RR# and the range too.

trigonometric functions:
#sin(x), cos(x)# : The domain is#RR# , the range#[1,1]#
#tan(x)# The domain is#RR{k pi/2}; k in ZZ# , the range is#RR#
Look at the unit circle, the distance between the xax and the intersection of the green and blue line is#tan(x)# , where#x# is the angle. If#x rarr pi/2# there is no intersection of the green and blue line, there#tan(x)# is not defined.
Remember that
graph{tan(x) [5, 5, 5, 5]}