1. Topic 1: Be able to combine functions and determine the resulting function. Topic 2: Be able to find the product of functions and determine the resulting function. Topic 3: Be able to perform multiple operations on functions. Topic 4: Determine if two given functions represent equivalent forms of the same function..

2. Equivalent Forms of Linear Functions Point Slope Form (PSF): Slope Intercept Form (SIF): Standard Form (SF): y = m(x - x 1 ) + y 1 y = mx + b Ax + By = C y = 2(x - 3) + 5 y = 2x - 1 -2x + y = - 1 Example 1: What are the equivalent forms of y = -3(x + 2) - 5 y = -3x – 6 - 5Distribute y = -3x – 11Combine Like Terms 3x + y = – 11-3x - y = 11 Example 2: What are the equivalent forms of y = ½(x - 8) + 2 y = ½x – 4 + 2Distribute y = ½x – 2Combine Like Terms -½x + y = – 2 -x + 2y = – 4 x - 2y = 4

3. Match the PSF equation in the 1st column to its equivalent SIF in the 2nd column and then its equivalent SF in the 3rd column. y = 5(x + 3) - 8 y = 5(x - 3) - 8 y = 5(x - 3) + 8 y = 5(x + 3) + 8 PSFSIF y = 5x + 23 y = 5x + 7 y = 5x - 23 y = 5x - 7 SF 10x - 2y = 46 10x - 2y = -46 10x - 2y = 14 10x - 2y = -14

4. Match the PSF equation in the 1st column to its equivalent SIF in the 2nd column and then its equivalent SF in the 3rd column. PSF SIF y = -3/4(x + 4) - 7 y = 3/4(x + 4) - 7 y = 3/4(x + 4) - 9 y = -3/4(x + 4) - 9 y = 3/4x - 6 y = 3/4x - 4 y = -3/4x - 10 y = -3/4x - 12 SF -3x + 4y = -24 3x + 4y = -48 3x + 4y = -40 -3x + 4y = -16

5. Equivalent Forms of Quadratic Functions Vertex Form (VF): Standard Form (SF): y = a(x - h) 2 + k y = ax 2 + bx + c y = -2(x + 3) 2 - 6 y = -2x 2 - 12x - 24 Example 3: What is the equivalent form of y = 4(x + 5) 2 + 2 y = 4(x + 5)(x + 5) + 2Expand x5 x 5 x 2 5x 25 y = 4(x 2 + 10x + 25) + 2 Box (Multiply) y = 4x 2 + 40x + 100 + 2 Distribute y = 4x 2 + 40x + 102Combine Like Terms Example 4: What is the equivalent form of y = -½(x - 2) 2 + 6 y = -½(x - 2)(x - 2) + 6Expand x-2 x x 2 -2x 4 y = -½(x 2 - 4x + 4) + 6 Box (Multiply) y = -½x 2 + 2x - 2 + 6 Distribute y = -½x 2 + 2x + 4Combine Like Terms

6. Match the VF equation in the 1st column to its equivalent SF in the 2nd column. y = -3(x - 4) 2 + 8 y = -3(x + 4) 2 + 8 y = -3(x - 4) 2 - 8 y = -3(x + 4) 2 - 8 y = -3x 2 - 24 x - 56 y = -3x 2 - 24x - 40 y = -3x 2 + 24x - 56 y = -3x 2 + 24x - 40 Vertex Form Standard Form

7. Match the VF equation in the 1st column to its equivalent SF in the 2nd column. Vertex Form Standard Form y = 1/2(x + 6) 2 - 12 y = -1/2(x + 6) 2 - 12 y = 1/2(x + 6) 2 + 12 y = -1/2(x + 6) 2 + 12 y = -1/2x 2 - 6 x - 6 y = -1/2x 2 - 6x - 30 y = 1/2x 2 + 6x + 6 y = 1/2x 2 + 6x + 30

8. y = -3(x - 4) 2 + 8 y = -3(x + 4) 2 + 8 y = -3(x - 4) 2 - 8 y = -3(x + 4) 2 - 8 y = -3x 2 - 24 x - 4 y = -3x 2 - 24x - 20 y = -3x 2 + 24x + 20 y = -3x 2 + 24x + 4 y = 1/2(x + 6) 2 - 12 y = -1/2(x + 6) 2 - 12 y = 1/2(x + 6) 2 + 12 y = -1/2(x + 6) 2 + 12 y = -1/2x 2 - 6 x - 6 y = -1/2x 2 - 6x - 30 y = 1/2x 2 + 6x + 6 y = 1/2x 2 + 6x + 30