The relationship between the percentage of frozen citrus crop, and the cost of box of oranges is an illustration of a linear function.
- <em>The linear equation of the function is: </em>
<em>.</em>
- <em>The inverse function is: </em>
<em> .</em>
- <em>A practical domain is from 0% to 100%</em>
- <em>A practical range is from 7 to 29.9 </em>
<u>A. Input quantity</u>
The input quantity is the percentage of frozen citrus crop
<u />
<u>B. Output quantity </u>
The output quantity is the cost of box of oranges
<u>C. The linear function</u>
We have:
<em>Calculate the slope of the function</em>
<em>The linear equation is calculated as follows:</em>
<u>D. Rewrite as y = mx + b</u>
We have:
Collect like terms
<em>The function is:</em>
<u>E. A practical domain</u>
The domain is the possible values of P. Because P is a percentage, its possible values are 0% to 100%.
The domain of the function is:
<u>F. A practical range</u>
When P = 0%
When P = 100%
Hence, the range of the function is:
G. The meaning of
The inverse function of g(P) is
So:
is the percentage of frozen citrus crop, when the cost is $12.
<u>H. The inverse formula</u>
We have:
Subtract 7 from both sides
Make P the subject
So, the inverse formula is:
Substitute 12 for c
Read more about linear equations at: