Question 95·Medium·Linear Functions
The function gives the total cost, in dollars, to print pages at a local print shop. According to this model, what is the cost, in dollars, of printing each individual page?
For linear cost functions on the SAT, rewrite or recognize them in the form . The constant term is the fixed starting amount, and the coefficient of the variable counting items (like pages, hours, or miles) is the per-unit cost or rate—this coefficient is usually the answer they want, so identify it directly to save time.
Hints
Think about fixed cost vs. per-page cost
If you print 0 pages, what does equal? That amount is the fixed fee, not the per-page cost.
Look at how the cost changes with pages
Compare and . How much more do you pay when you go from 0 pages to 1 page? That increase is the cost of one page.
Focus on the coefficient of
In a linear function like , the coefficient is the rate per unit (here, per page). Identify that coefficient in .
Desmos Guide
Use a table to see the per-page cost
Type C(p) = 18 + 0.12p into Desmos, then use the table feature (tap the gear icon and select "Table"). Look at the values of when increases from 0 to 1; the amount that the total cost increases by is the cost of one page.
Step-by-step Explanation
Interpret the structure of the cost function
The function is , where is the total cost in dollars and is the number of pages. This has the form .
Identify the fixed fee and the per-page part
The term 18 does not depend on , so it is the fixed fee you pay even if you print 0 pages. The term changes when changes, so it represents the part of the cost that depends on how many pages you print.
Connect the coefficient of to the cost per page
The cost for each page is the amount added to the total cost for every increase of 1 in , which is exactly the coefficient of in the expression . Therefore, the cost of printing each individual page is dollars.