View
223
Download
1
Category
Preview:
DESCRIPTION
3 Remember: When both sides of an inequality are multiplied or divided by a negative number the inequality is reversed. Remember: When both sides of an inequality are multiplied or divided by a negative number the inequality is reversed. –3 < 5 Multiply both sides by –1: 3 < –5 So we have to reverse the inequality sign: 3 > –5 Rules of Inequalities This means that if we were trying to solve the inequality We could not just multiply both sides by as we do not know if this is negative. What we do have to do, is multiply it by, which has to be positive.
Citation preview
Aims:• To practice sketching graphs of rational functions• To be able to solve inequalities by sketching and observation.• To be able to solve inequalities by using an algebraic method
Graphs Lesson 4
Starter
Example 2 Solve (x - 2)(3x – 1) ≤ 0
Solve x2 + x – 3 > 4x + 1.
3
Remember: When both sides of an inequality are multiplied or divided by a negative number the inequality is reversed.
–3 < 5
Multiply both sides by –1:
3 < –5
So we have to reverse the inequality sign:
3 > –5
Rules of Inequalities
This means that if we were trying to solve the inequality
We could not just multiply both sides by as we donot know if this is negative. What we do have to do, is multiply it by , which has to be positive.
3dcxbax
2dcx dcx
4
Methods to Solve Inequalities
There are two methods we will look at to solve rational function inequalities.
Method 1Algebraic method: multiply both sides by the denominator squared.Then solve the quadratic inequality.
Method 2Sketching method: sketch the rational function and the line y = 2, then look to see where the curve is greater than the line y = 2. Points of intersection will need to be found.
2123
xx
212 x
5
Example 1
Solve the inequality 2123
xx
Method 1
6
Method 2
1. Find the intercepts with the axes
2. Find the vertical asymptotes
3. Examine the behaviour as x tends to
Example 1
Solve the inequality 2123
xx
123
xxy
x y
7
4. Draw line y = 2 see where they cross
2123 Solve
xx
2123 So
xx when
Example 2
Solve the inequality 2)2)(1()4)(1(
xxxx
Method 1
9
Example 2
Solve the inequality 2)2)(1()4)(1(
xxxx
Method 2
1. Find the intercepts with the axes
2. Find the vertical asymptotes
3. Examine the behaviour as x tends to
)2)(1()4)(1(
xxxxy
First sketch
x y
10
4. Draw line y = 2 see where they cross
when2)2)(1()4)(1( So
xxxx
2)2)(1()4)(1( Solve
xxxx
11
1. Solve the inequality (you chose your favourite method or show me both?)
On w/b
223
xx
Do ex 5G page 71. then revision ex 5
12
Recommended