Given the parent function g(x)=log_{2}x .

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

f(x)=log_{2}(x−4)−2

f(x)=log_{2}(x)−2

f(x)=log_{2}(x+3)+4

f(x)=log_{2}(x−3)−2

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

jjennylove
Oct 29, 2018

#1**+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 = log_{2} ( 7 - 3) - 2 must be true....so....

0 = log _{2} ( 4) - 2 [ Note that log_{2} (4) = log 4 / log 2 = 2 ]

0 = 2 - 2

Which is true !!!!

Does this make sense ???

CPhill
Oct 29, 2018

#2**+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

#3**+3 **

Good question !!!!....note that....

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

So we have

-2 = log_{2} (4 - 3) - 2 add to to both sides

0 = log_{2} (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

#4**+2 **

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

jjennylove
Oct 29, 2018