Question #23a8d

1 Answer
seph
Oct 17, 2014

You divide your graph into 3 parts also.
One for the case when #x < 2#, one for #x = 2#, and another for #x > 2#

When #x < 2#, the equation we should follow is

#y = 3 -x#

Needless to say, this equation is linear.
To graph, select any 2 numbers that satisfy #x < 2#.
Substitute the values into the equation to get the corresponding #y# value.
Finally, connect the points.

For simplicity, let's choose #x = 1#, and #x = 0#.

#x = 1#
#=> y = 3 - (1)#
#=> y = 2#

#x = 0#
#=> y = 3 - (0)#
#=> y = 3#

Connect #(0, 3)# and #(1, 2)#. Extend one end to #-oo#.
Since the equation is only true for #x < 2#, extend the other
end until #x = 2#. However, make this end excluded by making
the point hollow.

When #x = 2#, the equation that should be followed is

#y = 2#.

Graph this by drawing a point at #(2, 2)#

Finally when #x > 2#, the equation that should be followed is

#y = x/2#

Again, this equation is linear.
Choose any two values of #x# that satisfy #x > 2# and substitute into the equation to get its corresponding #y# value.

For demonstration, let's choose #x = 4# and #x = 6#.

#x = 4#
#=> y = 4/2#
#=> y = 2#

#x = 6#
#=> y = 6/2#
#=> y = 3#

Connect the points #(4, 2)# and #(6, 3)#.
Extend this up to the point where #x = 2#.
Similar to the case when #x < 2#, make the point hollow.
Extend your other end indefinitely and you have your graph.

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