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X
- WE WANT TO COMPLETE THE TABLE USING
THE FUNCTION RULE F OF X = 3X - 2.
SO X IS OUR INPUT AND F OF X WOULD BE THE OUTPUT
OR THE SECOND COLUMN.
SO IF WE'RE GIVEN X = -1 WE WANT TO SUBSTITUTE -1 FOR X
TO DETERMINE THE FUNCTION VALUE.
SO WE WOULD HAVE 3 x -1 - 2, THIS WOULD BE -3 - 2 THAT'S -5.
SO THIS MEANS THAT F OF -1 IS = TO -5.
SO -1 IS THE INPUT AND -5 IS THE OUTPUT.
I THINK IT'S ALSO IMPORTANT TO RECOGNIZE THAT
THIS REPRESENTS A POINT THAT WOULD BE ON THE GRAPH
OF OUR FUNCTION.
IF F OF -1 IS = TO -5 THE FUNCTION WOULD CONTAIN
THE POINT WITH AN X-COORDINATE OF -1 AND A Y-COORDINATE OF -5.
REMEMBER F OF X IS = TO Y.
NEXT, WE HAVE X = 0.
SO OUR FUNCTION VALUE WOULD BE 3 x 0 - 2,
IT'S GOING TO BE -2.
SO THIS TELLS US THAT F OF 0 IS = TO -2
AND THAT THE GRAPH OF THE FUNCTION
WOULD CONTAIN THE POINT 0, -2.
AND X IS = TO 1 THE FUNCTION VALUE
WOULD BE 3 x 1 - 2.
THIS IS 3 - 2 SO THAT'S = TO 1.
SO WE HAVE F OF 1 = 1.
SO THE GRAPH OF THE FUNCTION WOULD CONTAIN THE POINT 1, 1.
AND X IS 2, WE HAVE 3 x 2 - 2 SO 6 - 2 THAT'S 4
SO F OF 2 IS = TO 4, WHICH MEANS THE GRAPH
OF THE FUNCTION WOULD CONTAIN THE POINT 2, 4.
AND THE LAST INPUT IS X = 3 SO WE'D HAVE 3 x 3 - 2,
9 - 2 IS 7 SO F OF 3 IS = TO 7, WHICH MEANS THE GRAPH
OF OUR FUNCTION WOULD CONTAIN THE POINT 3, 7.
SO YOU CAN SEE THAT TO EVALUATE A FUNCTION
WE'RE REALLY JUST PERFORMING SUBSTITUTION USING
THE GIVEN INPUT; BUT I THINK IT'S ALSO IMPORTANT
TO UNDERSTAND THE NOTATION HERE IN BLUE
AND THAT GRAPHICALLY IT REPRESENTS A POINT
ON THE GRAPH HERE IN RED.