- WE'RE GIVEN F OF X AND G OF X AND ASKED TO DETERMINE
THE FOLLOWING COMPOSITE FUNCTION VALUES.
IN THIS LESSON WE'LL DISCUSS
HOW WE CAN USE THE TI-84 GRAPHING CALCULATOR
TO DETERMINE THESE COMPOSITE FUNCTION VALUES.
WE'LL BEGIN BY ENTERING F OF X ON THE CALCULATOR AS Y SUB 1
AND G OF X AS Y SUB 2.
IT'S IMPORTANT THAT WE KNOW WHICH FUNCTION IS WHICH.
SO WE'LL PRESS Y =, AND AGAIN, Y SUB 1 IS GOING TO BE 5/8,
WHICH I'LL PUT IN PARENTHESES, x X - 5.
ENTER.
AND Y SUB 2 WILL BE G OF X, WHICH IS 3X TO THE 2nd - 2X + 7.
NOW WE'LL GO BACK TO THE HOME SCREEN
BY PRESSING SECOND MODE FOR QUIT.
LOOKING AT OUR FIRST COMPOSITE OF FUNCTIONS,
NOTICE HOW IT'S WRITTEN TWO WAYS.
THESE ARE THE TWO MOST COMMON WAYS
TO EXPRESS A COMPOSITE OF FUNCTIONS.
IN BOTH CASES WE SAY F OF G OF 2,
BUT I THINK THE SECOND NOTATION HERE
IS A LITTLE EASIER TO WORK WITH,
BECAUSE IT'S EASIER TO SEE
WHICH FUNCTION WOULD BE THE INNER FUNCTION.
NOTICE HERE THE OUTPUT OF G OF 2 WILL BECOME THE INPUT
INTO FUNCTION 4.
BUT IN OUR CASE, BECAUSE WE'RE USING A CALCULATOR,
THIS WOULD BE EQUIVALENT TO Y SUB 1 OF Y SUB 2 OF 2.
REMEMBER, F OF X = Y SUB 1, AND G OF X = Y SUB 2.
AND NOW WE'LL GO TO THE CALCULATOR TO ENTER THIS.
SO WE'RE GOING TO PRESS VARS, RIGHT ARROW, ENTER.
NOTICE HOW Y SUB 1 IS ALREADY HIGHLIGHTED,
SO WE'LL PRESS ENTER.
OPEN PARENTHESIS, AND NOW WE WANT TO SELECT Y SUB 2.
SO WE'LL PRESS VARS, RIGHT ARROW, ENTER,
GO DOWN TO NUMBER 2, PRESS ENTER,
ANOTHER OPEN PARENTHESIS, THE INPUT OF 2,
AND NOW WE HAVE TWO CLOSED PARENTHESES.
AND NOW WE CAN JUST PRESS ENTER.
THIS WOULD BE THE COMPOSITE FUNCTION VALUE.
BUT TO CONVERT THIS TO A FRACTION WE PRESS MATH,
ENTER, ENTER.
SO THIS COMPOSITE FUNCTION VALUE IS EQUAL TO 35/8.
NEXT WE HAVE G OF F OF 4.
AND AGAIN, WE CAN'T FORGET THAT F OF X = Y SUB 1,
AND G OF X = Y SUB 2.
SO HERE WE WOULD HAVE Y SUB 2 OF Y SUB 1 OF 4.
IT IS IMPORTANT THAT WE PAY CLOSE ATTENTION
TO THE ORDER OF COMPOSITION.
NOTICE HERE Y SUB 2 OR G OF X IS THE OUTER FUNCTION,
AND Y SUB 1 OR F OF X IS THE INNER FUNCTION.
SO GOING BACK TO THE CALCULATOR,
VARS, RIGHT ARROW, ENTER, Y SUB 2.
SO ARROW DOWN ONCE, ENTER, OPEN PARENTHESIS.
NOW WE WANT Y SUB 1, SO VARS, RIGHT ARROW, ENTER.
Y SUB 1 IS ALREADY HIGHLIGHTED, SO WE PRESS ENTER.
OPEN PARENTHESIS, THE INPUT OF 4, CLOSED PARENTHESIS,
CLOSED PARENTHESIS, AND ENTER.
WE WANT THE FRACTION VALUE OF THIS,
SO WE PRESS MATH, ENTER, ENTER, 123/4.
SO THE COMPOSITE FUNCTION VALUE IS 123/4.
NEXT WE HAVE F OF G OF 1/2,
WHICH WOULD BE Y SUB 1 OF Y SUB 2 OF 1/2.
SO VARS, RIGHT ARROW, ENTER.
Y SUB 1 IS ALREADY HIGHLIGHTED.
ENTER, OPEN PARENTHESIS.
NOW WE WANT Y SUB 2.
VARS, RIGHT ARROW, ENTER, SELECT Y SUB 2.
OPEN PARENTHESIS, 1/2 AS 1 DIVIDED BY 2,
CLOSED PARENTHESIS, CLOSED PARENTHESIS, AND ENTER.
TO CONVERT TO A FRACTION WE PRESS MATH, ENTER, ENTER.
-25/32 WOULD BE THE COMPOSITE FUNCTION VALUE.
AND FOR OUR LAST EXAMPLE WE HAVE F OF F OF 2/3,
WHICH WOULD BE Y SUB 1 OF Y SUB 1 OF 2/3.
SO ONE MORE TIME BACK TO THE CALCULATOR,
VARS, RIGHT ARROW, ENTER, ENTER FOR Y SUB 1, OPEN PARENTHESIS.
WE WANT Y SUB 1 AGAIN, SO VARS, RIGHT ARROW, ENTER, ENTER,
OPEN PARENTHESIS, THE INPUT OF 2/3, CLOSED PARENTHESIS,
CLOSED PARENTHESIS, AND ENTER.
AND ONE MORE TIME, MATH, ENTER, ENTER,
TO CONVERT TO A FRACTION, - 755/96.
F OF F OF 2/3 = -755 DIVIDED BY 96.
I HOPE YOU FOUND THIS HELPFUL.