IT'S MR. PIATEK!!!
Okay, just kidding, now that I have your attention, keep reading.
Hello there, and my name is John... La! Obviously.
Today I will be explaining on how to write an equation of a transformed function graph. What? That's possible? Well yes. After I explain it, this should be as easy as 3.14. ;)
Now let's start, shall we?
Firstly, you would determine the equation of g(x) in the form of
y = af [ b ( x - h ) ] + k
I probably need pictures..
There we go, okay. First we should plot the points of both f(x) and the transformed function, which we will call g(x).
f(x) g(x)
(8,10) (4,4)
(7,2) (0,0)
(6,10) (-4,4)
Still with me? Let's continue.
Now remember that formula I told you about? Yes? No? Here : y = af [ b ( x - h ) ] + k
We can find the Translations first, which are h and k.
h = -7
To find out what h is, we look at the difference from the original vertex and the transformed vertex of each function, horizontally.
k = -2
To find k we look at the difference from the original vertex and the transformed vertex of each function, vertically.
Now we can look at the stretches, a and b.
a = 1/2 (one half)
We get a by taking g(x)'s vertical distance and divide it by f(x)'s vertical distance.
4 ÷ 8 = 0.5 (or 1/2)
b = 1/4 (one fourth)
We get b by taking the horizontal distance of g(x) and dividing it by f(x)'s horizontal distance.
8 ÷ 2 = 4 , BUT we read b as opposite/ inverse. That is why it is 1/4.
Before we plug the formula in, h is also read as opposite/inverse.
Now we just simply plug it into the formula. y = af [ b ( x - h ) ] + k
y = ½f [ ¼ ( x + 7 ) ] - 2
Now you're all done!
That wasn't so hard, right?
Hope everybody did well on their tests that was on Friday!
PEACE OUT Y'ALL!
Just kidding,
Bye!
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