Question

The total cost, y, for Leah and x friends to go to an amusement park can be modeled by a

linear function. The amusement park charges an entrance fee of $45.25 per person and a
parking fee of $10 per car. Leah's car has seating for a maximum of 6 people.
What is the range of the function for this situation?
A
B
{1, 2, 3, 4, 5, 6)
{55.25, 100.50, 145.75, 191.00, 236.25, 281.50}
55.25 Sy s 281.50
с
D
1SXS 6

Answer 1

Range of the function is:

{55.25, 100.50, 145.75, 191.00, 236.25, 281.50}

Explanation:

Given that:

Seating capacity of the car = 6

Entrance fee per person = $45.25

Parking fee per car = $10

Leah is accompanied by
`x` friends.

So, the total cost can be modeled as the following linear function:

`y=45.25x+10`

Now, the value of
`x` i.e. number of friends going with Leah can be any of the following:

0, 1, 2, 3, 4 or 5 (because maximum capacity of the car is 6).

Leah is also going.

So, total number of people can be 1, 2, 3, 4, 5 or 6.

Therefore, the table of
`x, y` can be:

`\begin{center}\begin{tabular}{ c c}x & y \\ 1 & 55.25 \\ 2 & 100.50 \\ 3 & 145.75 \\ 4 & 191 \\ 5 & 236.5 \\ 6 & 281.50 \\\end{tabular}\end{center}`

Here, the value of
`y` is nothing but the range of the function.

Therefore, the range of the linear function is:

{55.25, 100.50, 145.75, 191.00, 236.25, 281.50}