Applied exercises: Linear functions

Max and Jana go on a trip to the game park "Oh My Deer" in Wild Brook. The entrance fee to the game park is $$ 5$ for two people. The game park offers the opportunity to buy special animal food for $$ 1$ at each enclosure to feed the animals.

(a) Determine how much Max and Jana have to spend for their trip if they want to buy either 5, 10 or 20 units of animal food in the game park. Create a table of values.

(b) Find a function $f (x)$ describing the costs of the trip in $$$ depending on the number $x$ of food units which Max and Jana buy.

(d) Max and Jana have $$ 14$ available at the beginning of their trip. Read off from the graph how much food they can buy.

For this task you need the following basic knowledge: Linear function

(a) If Max and Jana buy 5 units of food, they have to pay five times $$ 1$ in addition to the $$ 5$ entrance fee. So in total, they pay:

$ 5 + 5 \cdot $ 1 = $ 10

If they buy 10 units of food, they have to pay in total

$ 5 + 10 \cdot $ 1 = $ 15

For 20 units of food, the total costs are

$ 5 + 20 \cdot $ 1 = $ 25

The table of values hence is:

Units of food	5	10	20
Total costs	$10	$15	$25

(b) If $x$ is the number of food units Max and Jana buy, then the two must pay $x$ dollars for the food. With the entrance fee of $5$ dollars, the total costs are given by

f (x) = x + 5

(c)

(d) To read off the number of units, start horizontally from the $y$ -axis at the total costs of $$ 14$ until you reach the function graph. This point corresponds to a trip with $$ 14$ spent.

From this point on the graph you go down vertically until you reach the $x$ -axis. In this case you end up at $x = 9$ . This is the number of food units Max and Jana have to buy in order to spend $$ 14$ in total.

So Max and Jana can buy up to 9 food units.

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