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.
