Question

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

Answer 1

The function whose graph is given to us is:

`f(x)=\log (x-3)`

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:

`f(x)=\log (x+3)`

then at x=4 we have:

`f(x)=\log 7\\eq 0`

If:

`f(x)=\log x+3`

then at x=4 we have:

`f(x)=\log 4+3\\eq 0`

( since,
`\log 4>0`

If:

`f(x)=\log x-3`

then at x=4 we have:

`f(x)=\log 4-3\\eq 0`

since,

`0<\log 4<1\\\\Hence,\\\\-3<\log 4-3<1-3\\\\i.e.\\\\-3<\log 4-3<-2\\\\i.e.\\\\-3<f(4)<-2` )

Hence, the only function which satisfies this property is:

`f(x)=\log (x-3)`

since, at x=4

we have:

`f(x)=\log (4-3)\\\\i.e.\\\\f(x)=\log 1\\\\i.e.\\\\f(x)=0`

Hence, the answer is:

`f(x)=\log (x-3)`

Answer 2

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