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- WE'RE GOING TO COMPLETE A TABLE OF VALUES
AND GRAPH THE BASIC SQUARE ROOT FUNCTION
WHICH IS F OF X = SQUARED OF X.
BUT BEFORE WE COMPLETE THE TABLE OF VALUES
WE SHOULD DISCUSS TH DOMAIN OF THE GIVEN FUNCTION.
THE DOMAIN IS A SET OF ALL POSSIBLE INPUTS OR VALUES OF X
FOR THE FUNCTION.
AND WE KNOW THE SQUARE ROOT OF A NEGATIVE NUMBER
IS NOT GOING TO BE REAL
THEREFORE WE CAN SAY THAT THE DOMAIN WOULD BE X > OR = TO 0.
SO WE COULD ONLY USE VALUES
THAT ARE > OR = TO 0 FOR OUR T TABLE.
SO LET'S START BY USING THE X VALUES OF 0, 1, 2, 3, 4 AND 5
AND NOTICE HOW IF X IS NOT A PERFECT SQUARE
WE'RE NOT GOING TO BE ABLE TO EVALUATE THESE BY HAND
SO LET'S GO AHEAD AND USE OUR GRAPHING CALCULATOR.
TO DO THIS WE'RE GOING TO ENTER IN THE FUNCTION INTO Y1
SO PRESS Y = TYPE IN THE SQUARE ROOT FUNCTION
SO SECOND X SQUARED BRINGS UP THE SQUARE ROOT FUNCTION X
CLOSE PARENTHESIS
AND NOW IF WE PRESS GRAPH WE WILL GET A NICE GRAPH
OF THE FUNCTION
BUT WE ACTUALLY WANT POINTS ON THE FUNCTION
SO WE'LL USE THE TABLE FEATURE.
BEFORE WE DO THIS LET'S PRESS SECOND WINDOW FOR TABLE SET
AND MAKE SURE WE HAVE BOTH OF THESE ON AUTO.
IF THEY'RE NOT ON AUTO WE CAN GO AHEAD AND JUST GO DOWN
AND HIGHLIGHT THEM
SO IT'S FLASHING ON AUTO AND THEN PRESS ENTER.
AND THEN FROM HERE WE'RE GOING TO PRESS SECOND GRAPH
WHICH BRINGS UP AS YOU CAN SEE A TABLE OF VALUES.
AND NOW WE CAN SCROLL UP AND DOWN
AND FIND THE VALUES THAT WE NEED.
LET'S GO AHEAD AND RECORD THE CORRESPONDING Y VALUES
FOR X = 0 THROUGH 5.
-- SOME OF THESE VALUES ARE IRRATIONAL
SO WE'LL ROUND THESE TO TWO DECIMAL PLACES.
SO WHEN X IS 0, Y IS 0, WHEN X IS 1, Y IS 1
WHEN X IS 2, Y IS APPROXIMATELY 1.41.
SO WE HAVE 0, 1 APPROXIMATELY 1.41
AND THEN WHEN X IS 3, Y IS APPROXIMATELY 1.73,
WHEN X IS 4, Y IS 2
AND WHEN X IS 5, Y IS APPROXIMATELY 2.34.
SO AS YOU CAN SEE, BY LOOKING AT THE TABLE OF VALUES
IF WE HAD TO DO THIS BY HAND WE'D WANT TO SELECT X VALUES
THAT WERE PERFECT SQUARES SO Y SIMPLIFIED PERFECTLY.
SO THE NEXT PERFECT SQUARE WOULD ACTUALLY BE 9
SINCE 3 x 3 = 9 AFTER 9 WE'D HAVE 4 x 4 = 16.
NOTICE THE SQUARE ROOT OF 9 = 3
AND THE SQUARE ROOT OF 16 = 4.
SO IF I GO BACK TO THE CALCULATOR
NOTICE AS WE SCROLL DOWN THE Y --
ARE GOING TO BE IRRATIONAL
UNTIL WE REACH X = 9 AND THEN X = 16.
LET'S GO AHEAD AND PLOT SOME OF THESE POINTS
SO WE CAN SKETCH OUR GRAPH.
WE HAVE THE (0, 0) (1, 1) I'M GOING TO GO AHEAD
AND SKIP TO THE (4, 2) AND THEN WE HAVE THE (9, 3).
SO EVEN THOUGH WE'VE ONLY PLOTTED 5 POINTS,
THIS IS ENOUGH TO MAKE A NICE GRAPH.
F OF X = THE SQUARED OF X
WOULD LOOK SOMETHING LIKE THIS.
AND OF COURSE, WE CAN VERIFY THIS ON THE CALCULATOR
BY PRESSING THE GRAPH OPTION,
WHICH LOOKS JUST LIKE OUR GRAPH.
NOTICE HOW GRAPHICALLY WE CAN ALSO VERIFY THE DOMAIN.
ALL THE X VALUES OF THIS FUNCTION START AT 0
AND MOVE TO THE RIGHT SO X IS > OR = TO 0.
OKAY. I HOPE YOU FOUND THIS HELPFUL.