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# Given the parent function g(x)=log 2 x . Last question

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Given the parent function g(x)=log2x .

What is the equation of the function shown in the graph?

f(x)=log2(x−4)−2

f(x)=log2(x)−2

f(x)=log2(x+3)+4

f(x)=log2(x−3)−2

I tried figuring it out,i think it is B?

Oct 29, 2018

#1
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In   y  = log ( x - a)  + b

The ( x -a) part translates the graph left/right   and the "b" translates it up/down

(x - a)  translates the graph right  by a units

( x + a)  translates the graph left by  a units

+ b   translates the graph up by  b units

- b  translates the graph down by  b units

Notice that it appears the the  parent has been translated to the right by 3  units...

The thing that translates the parent to the right by 3  units must  be  " ( x - 3 ) "

So...it appears that the last answer is correct

To check this....note that  (7,0)  is on the graph...which means that

0  =  log2 ( 7 - 3)  - 2    must be true....so....

0 =  log 2 ( 4)  - 2        [  Note that  log2 (4)  =  log 4 /  log 2   =  2  ]

0  =  2  -  2

Which is true  !!!!

Does this make sense  ???

Oct 29, 2018
#2
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Yes that all makes sense. I have a question though, when we go to check it we can use any point which in this case would be (7,0) or (4,-2) to check the answer? If not, why would it only be (7,0)?

jjennylove  Oct 29, 2018
edited by jjennylove  Oct 29, 2018
#3
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Good question  !!!!....note that....

Every point on the graph should check...let's check  ( 4 , -2)

So we have

-2  =  log2 (4 - 3)  - 2       add to to  both sides

0  =  log2 (1)     ......  [ Note   log a (1)  always  = 0   ]  [ proof...check this  log (1) / log (2) ]

0  =  0

True  !!!!

So...we know we have the  correct equation

CPhill  Oct 29, 2018
edited by CPhill  Oct 29, 2018
#4
+921
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Awesome! Thank you for your explanation it has really helped me.   I have been wrtiing down everything so I remember .

jjennylove  Oct 29, 2018
#5
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