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- ON THIS PROBLEM HERE, WE WANT TO MATCH THE GRAPH ON THE LEFT
WITH THE CORRECT FUNCTION ON THE RIGHT.
AND WE'RE TOLD THE BLACK GRAPH OR THIS GRAPH HERE
IS THE PARENT FUNCTION.
WE CAN PROBABLY TELL FROM THE GIVEN FUNCTION ON THE RIGHT
THAT OUR PARENT FUNCTION IS F OF X = THE SQUARE ROOT OF X.
SO IF WE LOOK AT THE GRAPHS FOR A MOMENT,
COMPARING THE BLUE AND RED FUNCTION TO THE BLACK FUNCTION,
NOTICE HOW THEIR VERTICAL SHIFTS EITHER UP OR DOWN
AND THEN COMPARING THE GREEN AND PINK FUNCTION
TO THE BLACK FUNCTION NOTICE HOW THESE TWO
ARE SHIFTS LEFT OR RIGHT.
SO ALL THESE FUNCTIONS ON THE RIGHT
EITHER SHIFT A FUNCTION UP, DOWN, LEFT OR RIGHT.
SO LET'S DO A QUICK REVIEW OF VERTICAL AND HORIZONTAL SHIFTS.
IF Y = F OF X + D, AND D IS POSITIVE,
THE SHIFT WILL BE UP D UNITS AND IF Y = F OF X - D,
WHERE D IS POSITIVE, THE SHIFT WILL BE DOWN D UNITS.
SO WHAT THAT MEANS IS IF WE HAVE OUR PARENT FUNCTION HERE,
AND THE NEW FUNCTION IS G OF X = THE SQUARE ROOT OF X + D,
THIS WILL SHIFT A PARENT FUNCTION UP D UNITS
AND IF OUR NEW FUNCTION IS F OF X - D
OR THE SQUARE ROOT OF X - D, THE SHIFT IS DOWN D UNITS.
SO IF THE CONSTANT IS OUTSIDE THE SQUARE ROOT,
THEN WE'LL HAVE A SHIFT UP OR DOWN.
NOW THE OTHER CASE IS IF WE HAVE Y EQUALS F(X + C),
WHERE C IS POSITIVE,
AND IN THIS CASE THE SHIFT IS GOING TO BE LEFT C UNITS.
NOW THE DIRECTION HERE MIGHT BE THE OPPOSITE
OF WHAT YOU MIGHT THINK
BECAUSE IT SAYS X + C SO WE MIGHT THINK RIGHT,
BUT IT'S ACTUALLY LEFT C UNITS.
AND IF WE HAVE Y = F(X - C),
AGAIN WHERE C IS POSITIVE, THE SHIFT WILL BE RIGHT C UNITS.
SO AGAIN, REFERENCING THE PARENT FUNCTION
F OF X = THE SQUARE ROOT OF X,
IF WE HAVE F(X + 2), OR THE SQUARE ROOT OF (X + 2),
NOTICE HOW THE PLUS 2 IS UNDERNEATH THE SQUARE ROOT,
THE SHIFT IS GOING TO BE TO THE LEFT 2 UNITS.
AND IF THE FUNCTION IS F(X - 2), OR THE SQUARE ROOT OF (X - 2),
THE SHIFT WILL BE RIGHT 2 UNITS.
SO IF THE CONSTANT IS INSIDE THE SQUARE ROOT SYMBOL,
IT'S GOING TO BE LEFT OR RIGHT,
IF IT'S PLUS A CONSTANT, IT'S TO THE LEFT,
AND IF IT'S MINUS A CONSTANT, IT WILL BE TO THE RIGHT.
SO GOING BACK TO OUR EXAMPLE,
LET'S FIRST IDENTIFY THE BLUE AND RED FUNCTIONS.
REMEMBER BECAUSE THE SHIFT IS UP OR DOWN,
THAT MEANS THE CONSTANT WOULD BE OUTSIDE THE SQUARE ROOT
WHICH MEANS THE BLUE AND RED FUNCTION
MUST BE EITHER FUNCTION B OR FUNCTION D.
NOTICE B IS G OF X = THE SQUARE ROOT OF X + 4,
AND SINCE THE 4 IS OUTSIDE THE SQUARE ROOT,
IT'S GOING TO BE SHIFTED UP 4 UNITS
WHICH WOULD BE THE BLUE GRAPH.
THEN LOOKING AT D,
NOTICE HOW WE HAVE G OF X = THE SQUARE ROOT OF X - 4.
AGAIN THE MINUS 4 IS OUTSIDE THE SQUARE ROOT,
WHICH MEANS IT WILL BE SHIFTED DOWN 4 UNITS
WHICH IN THIS CASE WOULD BE THE RED FUNCTION.
WHICH LEAVES US WITH THE GREEN AND PINK FUNCTION
WHICH MUST BE EITHER "A" OR C.
WELL "A" IS G OF X = THE SQUARE ROOT OF (X + 4)
SO AGAIN WE MIGHT BE THINKING TO THE RIGHT 4 UNITS,
BUT IT'S ACTUALLY TO THE LEFT 4 UNITS.
THEREFORE THE GRAPH OF THIS FUNCTION
WOULD BE THE GREEN GRAPH.
AND THEN FOR C WE HAVE G OF X = THE SQUARE ROOT OF (X - 4),
AGAIN WE MIGHT BE THINKING TO THE LEFT 4 UNITS
BECAUSE IT'S MINUS 4
BUT IT'S ACTUALLY GOING TO BE TO THE RIGHT.
THEREFORE THE GRAPH OF THIS FUNCTION
WOULD BE THE PINK FUNCTION.
SO THE IDEA ON THIS QUESTION IS NOT TO GRAPH THESE
ON THE GRAPHING CALCULATOR, AND THEN MATCH THEM,
THE IDEA IS TO RECOGNIZE THE TYPE OF SHIFT
BASED UPON THE GIVEN FUNCTION.
OKAY, I HOPE YOU FOUND THIS HELPFUL.