What this lesson covers
- The three slots every linear-function-from-context question is asking you to fill
- Why you decide what x counts BEFORE you go looking for the rate
- The reverse question: they hand you f(w) = 28w + 40 and ask what a number means
- A practice problem where the quantity is going down
- The three ways a phrase ends up in the wrong slot
Questions worked in the video
- 0:17A climbing gym charges a one-time $40 registration fee, then $14 for each visit. Marisol registers once and goes twice a week. Which function gives the total she has paid after w weeks?
- 1:44In f(w) = 28w + 40, what do the 40 and the 28 represent in the context of the story?
- 2:19A print shop starts the month with 900 sheets of paper. Each poster uses 4 sheets and the shop prints 15 posters each day. Which function gives the sheets remaining after d days?
Chapters
- 0:00The story already contains the function
- 0:17A gym fee, a per-visit price, and w weeks
- 0:34The three slots, filled from the sentence
- 1:44The same function, read backwards
- 2:19Practice: 900 sheets and a shrinking stock
- 3:08Three ways a phrase lands in the wrong slot
- 3:25Recap
Lesson transcript
The narration of the video, word for word, under its chapter headings.
0:17A gym fee, a per-visit price, and w weeks
A climbing gym charges a one-time $40 registration fee, then $14 a visit. Marisol registers once and goes twice a week. Which function gives what she has paid after w weeks?
0:34The three slots, filled from the sentence
Three slots, and the story names all three. What does x count? The rate, in dollars per one x. And the starting value, the amount before any x at all. Find the x slot first, because the rate has to match it. Here w counts weeks. So the rate slot needs dollars per week, and $14 is per visit. Two visits a week, at $14 each, is $28 a week. That 28 goes in the rate slot. The $40 registration is one time, so it is the starting value. So f(w) = 28w + 40. Check it at one week. $40 to register, plus two visits at $14, is $68, and the function gives 68. That is B. Choice A left the rate per visit. C swapped the two slots. D charged the registration fee every single week. One more check, and it is free. Dollars per week times weeks gives dollars, and the 40 is already dollars. Choice C multiplies a one-time $40 by weeks, and dollar weeks is not a thing.
1:44The same function, read backwards
Same story, asked backwards. The function is handed to you, and the question asks what a number means. What is the 40? Set w to zero. 40 is what she has paid before a single week of visits, the registration fee. And the 28? Go from w equals zero to w equals one. 68 minus 40 is 28, so 28 is what one more week costs. Not what one visit costs. The rate always answers per one unit of x, whatever x is counting.
2:19Practice: 900 sheets and a shrinking stock
Your turn, ten seconds on the clock. Watch the units, and watch which way the count is going. 900 sheets to start, so that is the starting value. Here d counts days. 15 posters a day, 4 sheets a poster, is 60 sheets a day. And the paper is running out, so the rate is negative 60. 900 minus 60d. That is C. The other three. A used 4 sheets per poster as if d counted posters. B counted posters instead of sheets. And D has the shop ending the month with more paper than it started with.
3:08Three ways a phrase lands in the wrong slot
Three ways a phrase lands in the wrong slot. One, the nearest number wins, and per visit gets used where per week belongs. Two, a one-time fee gets multiplied by x. Three, a quantity going down gets a positive rate.
3:25Recap
Decide what x counts first. Then the rate, then the starting value. The story names all three.
Read the written version: the Linear functions strategy guide, then try 25 hard Linear functions questions with full explanations. Both are free, no account needed.