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IB DP Maths: AA HL复习笔记2.8.1 Solving Inequalities Graphically
Category:
IB课程
,
教材笔记
,
福利干货
Date: 2022年7月12日 下午12:01
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
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 G
DC
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
Worked Example
转载自savemyexams
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