How do you find the important points to graph #g(x)=2^x-3#?

1 Answer
Tony B
Oct 15, 2016

see explanation

Explanation:

Tony B

Set #y=2^x - 3#

At #y=0"; "2^x=3#

Taking logs

#xlog(2)=log(3) => x=log(3)/(log(2)) ~~1.58 # to 2 decimal places
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
At #x=0"; "y" "=" "2^0-3" " ->" "y" "=" " 1-3#

#y" "=" "-2#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#Lim_(x->+oo)y= lim_(x->+oo)2^x-3 ->oo-3=oo#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#Lim_(x->-oo) y=lim_(x->-oo)2^x-3 ->0-3=-3#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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