What are the excluded values for #y=7/(5x-10)#?

1 Answer
Rachel
Mar 28, 2017

#x=2#

Explanation:

The only excluded values in this problem would be asymptotes, which are values of #x# that make the denominator equal to #0#. Since we cannot divide by #0#, this creates a point that is "undefined" or excluded.

In the case of this problem, we are looking for a value of #x# that makes #5*x-10# equal to zero. So let's set that up:
#5x-10=0#
#color(white)(5x)+10color(white)(0)+10#
#5x=10#
#/5color(white)(x)##/5#
#x=10/5# or #2#

So, when #x=2#, the the denominator becomes equal to zero. So that's the value we must exclude to avoid an asymptote. We can confirm this using a graph
graph{y=7/(5x-10)}

See, the graph is getting closer and closer to #x=2#, but it can never reach that point.

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