1. Do Now
Graph 𝑓 𝑥 = −& 𝑥 2 , 𝑥<2 &−3𝑥+5, 𝑥≥2 State the Domain and Range

2. Objective
Odd and Even Functions
Using a Graph to Solve an Inequality

3. Even Function Symmetrical with the y – axis To Test Algebraically:
Substitute –x in place of x and simplify
If the function is exactly the same as the original then the function is EVEN
𝑦= 𝑥 𝑜𝑟 𝑦= 𝑥 𝑜𝑟 𝑦= 𝑥

4. Examples of Even Functions

5. Odd Function Symmetrical with the origin To Test Algebraically
Substitute –x in place of x and also –y in place of y
If the function is exactly the same as the original then the function is ODD
Think about
𝒚= 𝒙 𝟑

6. Examples of Odd Functions

7. Are the functions Odd. Even or neither?
𝑦= 1 𝑥

8. Are the functions Odd. Even or neither?
𝑦=2𝑥

9. Are the functions Odd. Even or neither?
𝑦= 𝑥 2 −3

10. Are the functions Odd. Even or neither?
𝑦= (𝑥−5) 3

11. 1.7 Solve an Inequality by Graphing
1. Graph and find zeros (where the graph crosses the 𝑥 axis) 2. Decide if we need the part of the graph above (y > 0) or below (y < 0) the x-axis 3. Shade the corresponding part of the 𝑥-axis 4. Write the solution.

12. Solve −𝑥 2 +4𝑥≤𝟎
Graph 𝑦= −𝑥 2 +4𝑥 Look where graph has y ≤𝟎 Shade x values where y ≤𝟎 Write Solution: (−∞, 0 ∪ 4, ∞)

13. Solve 𝑥 2 +5𝑥≤𝟎 To help you find the zeros of 𝑦≤𝑥 2 +5𝑥
Set inequality equal to zero
Factor and solve
𝑥 2 +5𝑥=0
𝑥 𝑥+5 =0
𝑥=0 𝑜𝑟 𝑥+5 =0
𝑥=0 𝑜𝑟 𝑥=−5
These zeros are where the graph crosses the 𝑥 axis
If A is positive the parabola is opening up
Draw a rough sketch
Shade x values where y ≤𝟎

14. Solve (𝑥−3) 2 −5<𝟎
Graph 𝑦= (𝑥−3) 2 −5 in a graphing calculator Find zeros (2nd CALC “zero”) Look where y<0 Shade x values Write Solution: 0.76<𝑥<5.24

15. YOU TRY: Solve 𝑥 2 −3𝑥−10≥𝟎 Graph y =𝑥 2 −3𝑥−10
Look and see where y ≥𝟎
Shade the x values
Write the solution.

16. 1.6 Graph piecewise functions
𝑓 𝑥 = 𝑥 𝑓𝑜𝑟 𝑥≤−2
2𝑥 𝑓𝑜𝑟 −2<𝑥<4
8−3𝑥 𝑓𝑜𝑟 𝑥≥4

17. You try: Graph 𝑓 𝑥 = 5+3𝑥 𝑓𝑜𝑟 𝑥≤−1 (𝑥−1) 2 𝑓𝑜𝑟 −1<𝑥<3
𝑓 𝑥 = 5+3𝑥 𝑓𝑜𝑟 𝑥≤−1
(𝑥−1) 2 𝑓𝑜𝑟 −1<𝑥<3
7−𝑥 𝑓𝑜𝑟 𝑥≥3