IB DP Maths: AA HL復習筆記2.8.1 Solving Inequalities Graphically

Category: IB課程, 教材筆記, 福利干貨 Date: 2022年7月12日下午12:01

Consider the inequality?f(x) ≤?g(x), where?f(x) and?g(x) are functions of?x
- if we?move?g(x) to the LHS?we get
  - f(x) –?g(x) ≤ 0
Solve?f(x) –?g(x) = 0 to?find the?zeros?of?f(x) –?g(x)
- These correspond to the?x-coordinates of the points of intersection of the graphs?y?=?f(x)?and?y?=?g(x)
To solve the inequality we can use a?graph
- Graph?y?=?f(x) –?g(x)?and label its zeros
- Hence find the intervals of?x?that satisfy the inequality?f(x) –?g(x) ≤ 0
  - These are the?intervals which satisfies the original inequality?f(x) ≤?g(x)
- This method is particularly useful when finding the intersections between the functions is difficult due to needing large?x?and?y?windows on your GDC

Remember to?flip the sign?of the inequality when you?multiply or divide?both sides by a?negative?number
- e.?1 < 2?→ [times both sides by (–1)] →?–1 > –2?(sign flips)
Never multiply or divide?by a?variable?as this could be?positive or negative
- You can only multiply by a term if you are certain it is always positive (or always negative)
  - The safest way?to rearrange is simply to add & subtract to move all the terms onto one side