How do you find the domain, x intercept and vertical asymptotes of #h(x)=log_4(x-3)#?

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Answer 1 · 2017-08-15T10:52:04

#"Domain": x > 3#

#x"-intercept": x = 4#

#"Vertical asymptote:"# #x = 3#

We have: #h(x) = log_(4)(x - 3)#

For the domain of this function, we must consider the argument of the logarithm.

The argument of any logarithmic number must be greater than #0#:

#Rightarrow x - 3 > 0#

#therefore x > 3#

The domain of #h(x)# is #x > 3#.

Then, let's set #h(x) = 0#:

#Rightarrow log_(4)(x - 3) = 0#

Using the laws of logarithms:

#Rightarrow x - 3 = 4^(0)#

#Rightarrow x - 3 = 1#

#therefore x = 4#

The #x#-intercept of #h(x)# is #x = 4#.

Now, we have already determined that the domain of #h(x)# is #x > 3#.

This means that the graph of #h(x)# will never touch the line at #x = 3#

The vertical asymptote of #h(x)# is #x = 3#.