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

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

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 2 𝑜𝑟 𝑦= 𝑥 4 𝑜𝑟 𝑦= 𝑥

Examples of Even Functions

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

Examples of Odd Functions

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

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

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

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

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.

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, ∞)

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

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

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.

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

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