Question

What function is graphed below?

Answer 1

Answer:

The function that is graphed is:

                     $f(x)=\log x+3$

Step-by-step explanation:

We could clearly observe from the graph that:

when x=1 we have the value of the function as: f(1)=3

This means that from the given options we will check which option satisfies this property.

1)

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

when x=1 we have:

$f(1)=\log 1-3)\\\\f(1)=\log (-2)$

As we know that the logarithmic function is not defined for the negative value.

Hence, this option is incorrect.

2)

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

when x=1 we have:

$f(2)=\log (1+3)\\\\f(2)=\log (4)=0.6040$

Hence, this option is incorrect.

4)

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

when x=1 we have:

$f(1)=\log 1-3\\\\f(1)=0-3\\\\f(1)=-3$

Hence, this option is incorrect.

3)

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

When we plot this function we get the same graph as shown.

Also f(1)=3

            Hence, this option is correct.

Answer 2

Because the graph is shifted up three units from the original mother function (f(x) = log x), and therefore, the answer is f(x) = log x + 3.