Question

What function is graphed below?

Answer 1

Answer:

The function whose graph is given to us is:

                $f(x)=\log (x-3)$

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:

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

then at x=4 we have:

$f(x)=\log 7\neq 0$

If:

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

then at x=4 we have:

$f(x)=\log 4+3\neq 0$

( since, $\log 4>0$

If:

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

then at x=4 we have:

$f(x)=\log 4-3\neq 0$

since,

$0$ )

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