Answer:
The function is 16x + 69
Domain of the function is [0, 5]
Range of the function is [69, 149]
Explanation:
Given - Jacob has 69 flowers for a big party decoration. In addition, he is
planning to buy some flower arrangements that have 16 flowers
each. All of the arrangements cost the same. Jacob is not sure yet
about the number of flower arrangements he wants to buy, but
he has enough money to buy up to 5 of them.
To find - Write a function to describe how many flowers Jacob can buy.
Find a reasonable domain and range for the function.
Proof -
Let us assume that,
The number of flower arrangements Jacob buys = x
Given that,
Each Flower arrangement have 16 flowers.
So,
x Flower arrangements have 16x flowers.
Also given that, Jacob has 69 flowers for a big party decoration.
So,
Total flowers Jacob can buy, y = 16x + 69
So,
The function is 16x + 69
Now,
Given that, Jacob can buy up to 5 flower arrangements
i.e. x ≤ 5
So,
Domain of the function is [0, 5]
Now,
When x = 0
y = 16(0) + 69 = 69
When x = 5
y = 16(5) + 69 = 149
So,
Range of the function is [69, 149]