A state park charges $5 per car, plus $1 per person as an admission fee. The total charged for a car with x people is f(x) = x + 5. How will the graph of this function change if the per car charge is changed to $8 per car?

The original function for the cost \( f(x) \) when the charge is $5 per car and $1 per person is given by:

\[
f(x) = x + 5
\]

Now, if the per car charge changes to $8 per car, the new function would be:

\[
f(x) = x + 8
\]

To understand how the graph changes, we can compare the two functions:

1. Original function: \( f(x) = x + 5 \)
2. New function: \( f(x) = x + 8 \)

The difference between these two functions is:

\[
f(x)_{\text{new}} - f(x)_{\text{old}} = (x + 8) - (x + 5) = 3
\]

This shows that the new function is 3 units higher than the original function for any value of \( x \).

Therefore, the graph of the function will shift vertically **up by $3**.

So, the correct answer is:

**The line will shift vertically up by $3.**