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- GIVEN THIS TABLE THAT REPRESENTS A FUNCTION,
WE WANT TO DETERMINE THE VALUE OF R
WHICH IS THE MISSING OUTPUT HERE WHEN THE INPUT IS +2.
THEN WE NEED TO WRITE A FUNCTION RULE
FOR THE ENTIRE TABLE.
AND JUST TO REVIEW, THESE X VALUES
WOULD REPRESENT THE INPUTS INTO THE FUNCTION
ALSO REFERRED TO AS THE DOMAIN.
AND THE SET OF VALUES IN THIS COLUMN
WOULD BE THE OUTPUTS CALLED THE RANGE OF THE FUNCTION.
SO TO DETERMINE THE VALUE OF R, THE FIRST THING WE WANT
TO RECOGNIZE IS THAT IF WE LOOK AT THE INPUTS
AS WE WORK OUR WAY DOWN THIS COLUMN NOTICE
THAT EACH OF THE INPUTS ARE INCREASING BY ONE.
AND NOW IF WE LOOK AT THE CORRESPONDING OUTPUTS,
NOTICE FROM 8 TO 4 IS A DECREASE OF 4 SO WE'RE SUBTRACTING 4 HERE
AND FROM 4 TO 0 WE'RE SUBTRACTING 4,
AND FROM 0 TO -4 WE'RE SUBTRACTING 4.
SO BY RECOGNIZING THIS PATTERN WE SHOULD BE ABLE TO DETERMINE
THE VALUE OF R.
IF WE HAVE -4 AND WE SUBTRACT 4 AGAIN THIS WOULD GIVE US
THE VALUE OF -8 FOR R AND LET'S SEE IF
THE PATTERN CONTINUES.
-8 - 4 DOES GIVE US -12 SO WE CAN CONCLUDE
THAT R IS EQUAL TO -8.
NOW WE WANT TO SEE IF WE CAN WRITE A FUNCTION RULE
THAT WOULD CREATE THIS ENTIRE TABLE.
WE DID JUST FINISH STUDYING LINEAR EQUATIONS
AND THIS TABLE DOES REPRESENT A LINEAR RELATIONSHIP.
SO BECAUSE OF THIS WE CAN ACTUALLY USE
THE SLOPE INTERCEPT FORM OF A LINE
TO HELP US DETERMINE THE FUNCTION RULE
FOR THIS TABLE.
SO WE'LL USE THE FORM OF A LINEAR EQUATION Y = MX + B
WHERE M IS THE SLOPE AND B IS THE Y-INTERCEPT.
REMEMBER F OF X IS EQUAL TO Y.
SO BY ANALYZING THIS TABLE NOW WE SHOULD BE ABLE
TO DETERMINE THE SLOPE AND THE Y-INTERCEPT.
REMEMBER THE SLOPE IS THE RATIO OF THE CHANGE OF Y
TO THE CHANGE OF X.
WELL, LOOKING AT OUR TABLE NOTICE THAT THE CHANGE OF Y
IS -4 WHEN THE CHANGE OF X IS + 1.
SO IF WE HAVE A -4/+1 THIS TELLS US THE SLOPE
WOULD BE -4.
AND SINCE B IS THE Y-INTERCEPT
WHICH OCCURS WHEN X IS EQUAL TO 0;
IF WE LOOK AT OUR TABLE NOTICE THAT WHEN X IS 0
Y IS EQUAL TO 0.
SO THIS TELLS US THAT THE Y-INTERCEPT
IS EQUAL TO 0 AND THEREFORE B IS EQUAL TO 0.
SO THE LINEAR EQUATION IN THE SLOPE INTERCEPT FORM
THAT WOULD PRODUCE THIS TABLE WOULD BE Y = -4 x X OR -4X.
AND NOW WE CAN WRITE THIS USING FUNCTION NOTATION
BY SIMPLY REPLACING Y WITH F OF X.
SO THE FUNCTION RULE FOR THIS TABLE
WOULD BE F OF X = -4X.
SO WHENEVER WE HAVE A TABLE THAT'S A LINEAR RELATIONSHIP
WE CAN WRITE THE EQUATION IN SLOPE INTERCEPT FORM
AND THEN WRITE THE EQUATION AS A FUNCTION RULE.
AND OF COURSE WE CAN TEST THIS IF WE WANT WITH AN INPUT OF -2.
THE OUTPUT WOULD BE +8, THAT CHECKS.
IF THE INPUT IS -1, WE'D HAVE -4 x -1,
WHICH IS +4 AND SO ON.
OKAY, I HOPE YOU FOUND THIS HELPFUL.