- HERE WE ARE GIVEN A TABLE THAT REPRESENTS A FUNCTION.
WE WANT TO DETERMINE THE VALUE OF Y,
WHICH IS THIS MISSING OUTPUT HERE WHEN THE INPUT IS +1.
THEN WE WANT TO WRITE A FUNCTION RULE
FOR THE ENTIRE TABLE.
SO IN THIS CASE THESE VALUES OF N
WOULD BE THE INPUTS INTO THE FUNCTION.
THESE VALUES ARE ALSO THE DOMAIN OF THE FUNCTION
AND THE VALUES IN THE SECOND COLUMN
WOULD BE THE OUTPUTS OF THE FUNCTION
ALSO CALLED THE RANGE OF THE FUNCTION.
LOOKING AT THIS FIRST COLUMN WE NEED TO BE ABLE TO RECOGNIZE
THAT N IS INCREASING BY 1 EACH TIME.
-2 + 1 DOES EQUAL -1, -1 + 1 IS EQUAL TO 0,
0 + 1 IS 1, 1 + 1 IS 2, AND 2 + 1 IS 3.
NOW, LETS TAKE A LOOK AT F OF N OR THE OUTPUTS.
WE HAVE -5, -4, -3, AN UNKNOWN VALUE, -1, AND 0.
WELL, FROM -5 TO -4 THAT'S AN INCREASE OF 1,
-4 TO -3 IS ALSO AN INCREASE OF 1
SO IF THIS PATTERN CONTINUED Y WOULD BE EQUAL TO -3 + 1,
WHICH WOULD BE EQUAL TO -2.
LET'S GO AHEAD AND WRITE THAT DOWN.
WE THINK Y IS EQUAL TO -2 AND LET'S SEE
IF THE PATTERN CONTINUES.
-2 + 1 IS -1 AND -1 + 1 IS 0 AND NOW WE CAN CONCLUDE
THAT Y IS EQUAL TO -2.
NOW WE DID JUST FINISH STUDYING LINEAR EQUATIONS.
AND NOTICE THAT IN THIS TABLE IF WE TREAT THIS FIRST COLUMN
AS X AND THE SECOND COLUMN AS Y; NOTICE THAT THE RATIO
OF THE CHANGE OF Y TO THE CHANGE OF X
IS CONSTANT WHICH SHOULD REMIND US OF A LINEAR EQUATION.
SO WHAT WE'LL DO IS WRITE THE EQUATION
FOR THIS TABLE IN SLOPE INTERCEPT FORM,
OR Y = MX + B FORM, AND THEN ONCE WE HAVE
THE EQUATION IN TERMS OF X AND Y WE'LL WRITE THE FUNCTION RULE
USING FUNCTION NOTATION.
REMEMBER THAT M IS THE SLOPE OF THE LINE
AND B IS THE Y-INTERCEPT OF THE LINE.
AGAIN, M IS THE RATIO OF THE CHANGE OF Y
TO THE CHANGE OF X.
LOOKING AT OUR TABLE NOTICE THE CHANGE IN Y IS +1
WHEN THE CHANGE OF X IS ALSO +1.
SO OUR SLOPE WOULD BE 1/1, WHICH IS JUST 1.
AND THEN B, THE Y-INTERCEPT OCCURS WHEN X IS EQUAL TO 0.
LOOKING AT THIS ROW IN THE TABLE,
NOTICE THAT WHEN X IS 0 THE Y VALUE, OR THE OUTPUT,
WOULD BE -3 WHICH MEANS B IS EQUAL TO -3.
SO PUTTING THESE PIECES TOGETHER,
THE LINEAR EQUATION WOULD BE Y = 1 x X.
AND THEN SINCE B IS -3, WE'D HAVE - 3 OR WE COULD
JUST WRITE Y = X - 3.
BUT REMEMBER OUR GOAL WAS TO WRITE THE RULE
USING FUNCTION NOTATION.
SO WE CAN REPLACE Y WITH F OF N.
SO WE'D HAVE F OF N = AND WE'LL REPLACE X WITH N
SO WE HAVE N - 3.
THIS WOULD BE OUR FUNCTION RULE FOR THE GIVEN TABLE.
AND JUST TO BE SURE, WE COULD EVALUATE THIS FUNCTION
AT THE GIVEN INPUTS.
IF THE INPUT IS -2, THE OUTPUT IS GOING TO BE -2 - 3
WHICH IS -5.
LET'S GO AHEAD AND JUST CHECK ONE MORE.
WHEN N IS EQUAL TO 2 THE INPUT IS 2
AND NOTICE THAT 2 - 3 IS EQUAL TO -1
SO OUR FUNCTION RULE IS CORRECT.
I HOPE YOU FOUND THIS HELPFUL.