– WE WANT TO DETERMINE

THE EQUATION FOR THE EXPONENTIAL FUNCTION

FROM THE GRAPH USING A FORM OF F OF X=”A” x B

RAISED TO THE POWER OF X. BUT THIS ONE’S A LITTLE MORE

INVOLVED THAN THE OTHER EXAMPLES BECAUSE NOTICE HOW THIS GRAPH

DOES HAVE A HORIZONTAL ASYMPTOTE OF Y=+4. WHICH MEANS

THE EXPONENTIAL FUNCTION WOULD HAVE TO BE SHIFTED UP

4 UNITS IN ORDER TO HAVE THIS

HORIZONTAL ASYMPTOTE. THIS GRAPH ALSO APPEARS TO BE

EXPONENTIAL DECAY THAT’S BEEN REFLECTED

ACROSS THE X AXIS. SO WE SHOULD RECOGNIZE

THAT THE VALUE OF “A” IS GOING TO BE NEGATIVE, BUT IF NOTHING ELSE

WE DO HAVE TO RECOGNIZE THAT THE EXPONENTIAL FUNCTION

HAS BEEN SHIFTED UP 4 UNITS BECAUSE OF THIS

HORIZONTAL ASYMPTOTE, WHICH MEANS OUR EXPONENTIAL

FUNCTION WILL BE IN THE FORM OF F OF X=”A” x B RAISED

TO THE POWER OF X + 4. SO ONCE WE RECOGNIZE THIS, THEN WE CAN DETERMINE THE VALUES

OF “A” AND B BY IDENTIFYING TWO POINTS

ON THE FUNCTION THAT WILL GIVE US

TWO FUNCTION VALUES. SO NOTICE HOW THIS POINT HERE

OR THE Y INTERCEPT IS (0, 2) AND THIS POINT HERE

IS THE POINT (-1, -4) WHICH MEANS IF THE FUNCTION

CONTAINS THE POINT (0, 2) F OF 0 MUST=2 AND IF THE FUNCTION CONTAINS

THE POINT (-1, -4) THEN F OF -1 MUST=-4. NOW THAT WE KNOW F OF 0=2 WE SHOULD BE ABLE TO USE THIS

TO DETERMINE THE VALUE OF “A” AND THEN WE CAN USE

THE SECOND FUNCTION VALUE TO DETERMINE THE VALUE OF B. SO IF F OF 0=2

WE’LL REPLACE X WITH 0. SO WE WOULD HAVE “A” x B

TO THE 0 + 4 MUST EQUAL +2. WELL, B TO THE 0 IS EQUAL TO 1 SO WE HAVE “A” + 4=2,

SUBTRACT 4 ON BOTH SIDES. SO WE HAVE “A”=-2. SO NOW WE KNOW THAT F OF X MUST EQUAL -2 x B

TO THE POWER OF X + 4. NOTICE HOW “A” IS NEGATIVE

WHICH IS WHAT WE THOUGHT BECAUSE IT DOES LOOK LIKE THIS

IS EXPONENTIAL DECAY REFLECTED ACROSS THE X AXIS. SO NOW WE’LL USE THIS FORM

OF OUR FUNCTION AND OUR SECOND FUNCTION VALUE

TO DETERMINE THE VALUE OF B AND LET’S GO AHEAD AND DO THAT

ON THE NEXT SLIDE. SO WE WERE ABLE TO USE F OF 0=

2 TO DETERMINE THE VALUE OF “A” AND NOW WE’LL USE F OF -1=-4

TO DETERMINE THE VALUE OF B. SO F OF -1 IS GOING TO BE EQUAL

TO -2 x B TO THE -1 + 4 WHICH MUST EQUAL -4. SO THE FIRST STEP, LET’S GO AHEAD AND SUBTRACT 4

ON BOTH SIDES. SO WE HAVE -2 B TO THE -1=-8. I’M GOING TO MAKE THIS

INTO A FRACTION AND REMEMBER IF I MOVE THE B

DOWN TO THE DENOMINATOR IT’S GOING TO CHANGE THE SIGN

OF THE EXPONENT. SO WE WOULD HAVE -2/B=-8 AND NOW WE’RE GOING TO MULTIPLY

BOTH SIDES OF THE EQUATION BY B. THIS IS B/1

SO THE Bs SIMPLIFY OUT. WE HAVE -2=-8B. NOW WE CAN DIVIDE BOTH SIDES

BY -8. SO WE HAVE B

=THIS SIMPLIFIES TO +1/4. SO NOW THAT WE HAVE B

WE HAVE OUR FUNCTION. OUR FUNCTION IS F OF X

=-2 x THE BASE OF 1/4 RAISED TO THE POWER OF X + 4. NOW HOPEFULLY WE RECOGNIZE THAT BECAUSE THE BASE IS BETWEEN

0 AND 1 WE HAVE EXPONENTIAL DECAY. BECAUSE “A” IS NEGATIVE IT’S

REFLECTED ACROSS THE X AXIS. BECAUSE OF THE 2 IT’S BEEN

VERTICALLY STRETCHED AND BECAUSE OF THE +4

IT’S BEEN SHIFTED UP 4 UNITS AND THESE TRANSFORMATIONS DO DESCRIBE THE PROVIDED GRAPH

IN RED. I HOPE YOU FOUND THIS HELPFUL.

Bro, I'm pretty sure you just saved me for my math test today.

thnx that helps alotย

Thank you, you have no idea how much this helped me out!

thank you so much this is wonderful

THANK YOU!!!

MY BRAIN IS STRONG NOW!!!

THANKS YOU SO MUCHHHH!!! I've been looking for this for soo looongggg

thankss

Thank you so much.

Nice ๐

Thanks!

wow thanks! I'm so ready for my math test now

what do you do if your first f(x) doesn't have f(0)? Then you have both an a and a b in the equation. ๐

i need help still when the exponential graph is shifted horizontally

What if the y-intercept is below 1??

this was also a great video

You're actually a lifesaver

Legend

Extremely helpful

Any videos for finding an exponential equation with a Vertical Asymptote?

00:05 "Using a form of f(x) times Ayyyyyyyyyyy times b raised to the power of x."