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?

Question

The line will shift vertically down by $3.
The line will shift vertically up by $3.
The line will shift vertically up by $8.
The line will shift vertically down by $8.

Answer 1

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.