How do I graph by applying the piece wise definitions?

Question

Y= (4|x-3|)/(x-3)

Answer 1

first, x=3 is NOT IN THE DOMAIN.

 

second, if x > 3, then this function is just y = 4...you can graph that, on the interval (3, infinity)

 

third, if x < 3, then the absolute value desired is -(x-3) so then this function is just y = -4...you can graph that, on the interval (-infinity, 3)

Answer 2

As Kenneth said:

Since dividing by zero is undefined

We have a vertical asymtope at x=3

 

For x>3 the |x-3| = x-3 giving

y= 4(x-3)/(x-3) = 4

Thus, for all x>3 just graph the horizontal line y=4

 

However... For x<3 the |x-3| = -(x-3) = 3-x

so the value for x<3 is

y = 4(3-x)/(x-3)

= -4(x-3)/(x-3) = -4

 

Note: No different than Kenneth's answer.  Just wanted to

show a little bit more of how he got there.  Also,  don't 

forget to put the open circle at x=3 on both parts of the

graph to indicate that the point is not actually included.