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What function is graphed below?


f(x) = log (x − 3)
f(x) = log (x + 3)
f(x) = log x + 3
f(x) = log x − 3

What function is graphed below fx log x 3 fx log x 3 fx log x 3 fx log x 3 class=

Respuesta :

carlosego
The answer for the exercise shown above is the first option, which is:
 f(x)=log(x-3) 
 The explanation is shown below:
 If you substitute the x in the function for values, you will obtain the graph attached above. As you can see on the mentioned graph, when the variable x has the value 4, the value y is 0. Therefore, you have:
  f(x)=log(x-3) 
  f(x)=log(4-3) 
  f(x)=log(1)
  f(x)=0
 

Answer:

The function whose graph is given to us is:

                [tex]f(x)=\log (x-3)[/tex]

Step-by-step explanation:

By looking at the graph of the function f(x) we observe that when x=4 then the value of the function is zero.

                  i.e. f(x)=0 at x=4.

( If:

[tex]f(x)=\log (x+3)[/tex]

then at x=4 we have:

[tex]f(x)=\log 7\neq 0[/tex]

If:

[tex]f(x)=\log x+3[/tex]

then at x=4 we have:

[tex]f(x)=\log 4+3\neq 0[/tex]

( since, [tex]\log 4>0[/tex]

If:

[tex]f(x)=\log x-3[/tex]

then at x=4 we have:

[tex]f(x)=\log 4-3\neq 0[/tex]

since,

[tex]0<\log 4<1\\\\Hence,\\\\-3<\log 4-3<1-3\\\\i.e.\\\\-3<\log 4-3<-2\\\\i.e.\\\\-3<f(4)<-2[/tex] )

Hence, the only function which satisfies this property is:

[tex]f(x)=\log (x-3)[/tex]

since, at x=4

we have:

[tex]f(x)=\log (4-3)\\\\i.e.\\\\f(x)=\log 1\\\\i.e.\\\\f(x)=0[/tex]

Hence, the answer is:

                          [tex]f(x)=\log (x-3)[/tex]

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