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- WE WANT TO DETERMINE THE FUNCTION VALUES
USING THE GRAPH PROVIDED.
THE MAIN THING TO REMEMBER HERE
IS THAT WHEN WRITTEN IN FUNCTION NOTATION,
FOR EXAMPLE F OF -5, THE -5 IS THE INPUT
WITH THE VALUE OF X AND THE FUNCTION VALUE OF THE OUTPUT
WOULD BE THE CORRESPONDING Y VALUE.
SO TO EVALUATE F OF -5,
WE'LL FIRST LOCATE -5 ON THE X AXIS WHICH IS HERE
AND THEN LOCATE THE POINT ON THE FUNCTION WHEN X = -5
WHICH WOULD BE THIS POINT HERE
AND THIS POINT WOULD HAVE A Y VALUE OR A Y COORDINATE OF 3
WHICH WOULD BE OUR FUNCTION VALUE.
THIS POINT HAS THE COORDINATES -5, 3 SO F OF -5 = 3.
NEXT WE HAVE F OF 2, SO THE INPUT OR THE X VALUE IS 2,
WELL HERE'S 2 ON THE X AXIS
SO WE'LL FIND THE POINT ON THE GRAPH WHEN X = 2
WHICH IS THIS POINT HERE.
AND WE CAN SEE THE Y COORDINATE
OR THE FUNCTION VALUE WOULD BE ONE A HALF OR 1.5.
THIS POINT HAS AN X COORDINATE OF 2,
AND A Y COORDINATE OF 1.5, THEREFORE F OF 2 = 1.5.
THE LAST EXAMPLE WE HAVE F OF 1 SO X = 1.
WE WANT TO DETERMINE THE FUNCTION VALUE
OR CORRESPONDING Y VALUE.
SO WE'LL FIRST LOCATE 1 ON THE X AXIS WHICH IS HERE.
NOTICE THAT X = 1, THERE'S A BREAK IN THE GRAPH,
SO HERE WE HAVE AN OPEN POINT AND HERE WE HAVE A CLOSED POINT
AND THE FUNCTION IS DEFINED
WHERE THE CLOSED POINT IS HERE NOT WHERE THE OPEN POINT IS.
SO WHEN X = 1, WE'RE ACTUALLY DOWN HERE ON THE FUNCTION
AND THE CORRESPONDING Y VALUE WE CAN SEE IS -3.
THIS POINT HAS AN X COORDINATE OF 1 AND A Y COORDINATE OF -3,
THEREFORE F OF 1 = -3.
I HOPE THIS EXPLANATION WAS HELPFUL.