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Linear functions
I worked these out from the practice questions. Each code says where to start reading, where to stop, what you can skip, and why it is safe.
1. Replace, do not think
- Start:
- The function and the input
- Stop:
- After you have replaced x and calculated
- Skip:
- The story around it
- Why:
- For f(5), just replace and calculate (question 1).
Used in question 1
2. The number with the letter is the rate
- Start:
- The function in a story question
- Stop:
- When you can say the meaning of the multiplier
- Skip:
- The other options before you decide
- Why:
- The multiplier of the input is the change per unit; the plain number is the start (question 2).
Used in question 2
3. Slope first, then walk
- Start:
- Both given points
- Stop:
- When you reach the asked input
- Skip:
- Finding b if you can step along
- Why:
- Find slope, then add slope for each step of x. It is often faster than the full rule (questions 3, 5, 7).
Used in questions 3, 5, 7
4. Output given? Make an equation
- Start:
- The line that gives f(a) = number
- Stop:
- After you solve for a
- Skip:
- Computing other values
- Why:
- Write the rule equal to the given output and solve (question 4).
Used in question 4
5. Break-even: set rules equal
- Start:
- The two rules in the question
- Stop:
- When you solve for n
- Skip:
- The words about profit
- Why:
- Equal income and cost means set the two rules equal (question 6).
Used in question 6
6. Difference form means slope
- Start:
- The line h(x + 3) − h(x) = 12
- Stop:
- When you divide to get the slope
- Skip:
- The 'for every x' idea
- Why:
- A change in output over a change in input is the slope (question 8).
Used in question 8
7. Desmos table check
- Start:
- The rule or the two points
- Stop:
- When the graph passes the two points
- Skip:
- Hand algebra if time is short
- Why:
- Type the two points in Desmos, it draws the line, and you read the third value (questions 3, 5, 7).
Used in questions 3, 5, 7
8. Graph: read two clean points, then slope
- Start:
- The labelled points or the places where the line crosses the grid
- Stop:
- When you have slope and the y-intercept
- Skip:
- The picture beyond those points
- Why:
- Pick two points you can read exactly, work out rise over run, and write the rule. The rest of the question then needs only the rule (questions 9, 13, 15, 16).
Used in questions 9, 13, 15, 16
9. Table of a line: constant step
- Start:
- The first two rows of the table
- Stop:
- When you see how much the output moves for one step of x
- Skip:
- The other rows once the pattern is clear
- Why:
- The row with x = 0 gives the starting value and the step gives the slope (questions 10 and 14).
Used in questions 10, 14
10. f(a) = b: input first, output second
- Start:
- The notation f(15) = 40 or T(m) = 50
- Stop:
- When you say the input and the output in words
- Skip:
- The long description of the model
- Why:
- The number inside the brackets is the input and the other number is the output. Say it aloud in the units of the story (questions 11 and 12).
Used in questions 11, 12