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avatar+708 

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

 

A coordinate graph with x axis ranging from negative 1 to 9 in increments of 1 and y axis ranging from negative 6 to 2 in increments of 1. The vertical axis is labeled as f of x. A logarithmic curve increasing from left to right beginning in the fourth quadrant and extending through the first quadrant. The graph begins very close to the vertical asymptote x equals three. As x increases y increases through the points begin ordered pair 4 comma negative 2 end ordered pair and begin ordered pair 7 comma 0 end ordered pair and on to positive infinity. The curve has arrows at both ends.

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

 Oct 29, 2018
 #1
avatar+98044 
+2

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  ???

 

 

cool cool cool

 Oct 29, 2018
 #2
avatar+708 
+1

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
avatar+98044 
+3

 

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

 

 

cool cool cool

CPhill  Oct 29, 2018
edited by CPhill  Oct 29, 2018
 #4
avatar+708 
+2

Awesome! Thank you for your explanation it has really helped me. smiley  I have been wrtiing down everything so I remember .

jjennylove  Oct 29, 2018
 #5
avatar+98044 
0

OK....glad to help....!!!!

 

 

cool cool cool

CPhill  Oct 29, 2018

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