IB DP Maths: AA HL复习笔记2.8.1 Solving Inequalities Graphically
How can I solve inequalities graphically?
- 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
- if we move g(x) to the LHS we get
- 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
Be careful when rearranging inequalities!
- 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
- You can only multiply by a term if you are certain it is always positive (or always negative)
Worked Example
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