How do you find the domain and range of #y=2x^2 - 4x - 5#?

1 Answer
Apr 3, 2018

Answer:

Ask yourself where the function is defined.

Explanation:

In your case the domain is the whole real ax #RR# and the range too. This is typical for all polynomials.
my_pic
Other examples:

  • logarithmic functions: #f(x)=log(x)#
    logarithmic functions are not defined for non positive argument so check where the argument is #<=0#.

#log(x-2)# #rArr# #x-2=0# , #x=2#
#x-2<=0# , #x<=2#
#f(x)# is defined for #x<=2#, so the domain is #(2, infty)#
The range is #RR#.
my_pic

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

  • trigonometric functions:

    • #sin(x), cos(x)#: The domain is #RR#, the range #[-1,1]#
      my_pic
    • #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 x-ax 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. my_pic

Remember that #tan(x)# has a period #pi#.
graph{tan(x) [-5, 5, -5, 5]}