How do you find the domain, x intercept and vertical asymptotes of #f(x)=ln(3-x)#?

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Answer 1 · 2017-03-06T09:34:04

The domain is #x in ]-oo,3[#
The x intercept is #=(2,0)#
The vertical asymptote is #x=3#

What's under the #ln# is #>0#.

So,

#3-x>0#

#x<3#

The domain of #f(x)# is #x in ]-oo,3[#

When #f(x)=0#

#ln(3-x)=0#

#ln1=0#

#3-x=1#

#x=3-1=2#

The x intercept is #=(2,0)#

As #x!=3#

The vertical asymptote is #x=3#

graph{(y-ln(3-x))(y-1000(x-3))=0 [-3.033, 4.76, -1.84, 2.056]}