 # 1.3 Families of Equations. What families of graphs have your studied? Linear Absolute Value Quadratic Square Root Cubic Cube Root.

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1.3 Families of Equations

What families of graphs have your studied? Linear Absolute Value Quadratic Square Root Cubic Cube Root

How do you recognize the various families? Linear Family Equation: Graph: y = mx + b Ax + By + C = 0 Line: m = + m = – m = 0

Examples: Graph the following linear equations: y = 3x - 5 Domain-- Range-- Increasing/Decreasing? Odd/Even

Examples: Graph the following linear equations: 2x – 3y = 12 Domain-- Range-- Increasing/Decreasing? Odd or Even?

How do you recognize the various families? Absolute Value Family Equation: Graph: y = a|x – h| + k (h,k) a = – a = +

Examples: Graph the following absolute value equations: y = |x| Domain-- Range-- Increasing/Decreasing? Odd or Even?

Examples: Graph the following absolute value equations: y = |x - 2|+ 3 Domain-- Range-- Increasing/Decreasing? Odd or Even

Examples: Graph the following absolute value equations: y = |x + 6|+ 5 Domain-- Range-- Increasing/Decreasing? Odd or Even

Examples: Graph the following absolute value equations: y = -|x - 1|-3 Domain-- Range-- Increasing/Decreasing? Odd or Even?

How do you recognize the various families? Quadratic Family Equation: Graph: Pattern: y = a(x – h) 2 + k y = ax 2 + bx + c a = – (h,k) a = + (h,k) 1, 3, 5

Examples: Graph the following quadratic equations: y = x 2 Domain-- Range-- Increasing/Decreasing? Odd or Even

Examples: Graph the following quadratic equations: y = (x-1) 2 Domain-- Range-- Increasing/Decreasing? Odd or Even?

Examples: Graph the following quadratic equations: y = -(x-2) 2 + 4 Domain-- Range-- Increasing/Decreasing Odd or Even?

Examples: Graph the following quadratic equations: y = x 2 + 4x - 1 Hint: x = -b 2a

How do you recognize the various families? Square Root Family Equation: Graph: Pattern: a = – a = + y = a√x – h + k (h,k) or (h,k) or 1, 3, 5 y = a(x – h) 1/2 + k

Examples: Graph the following square root equations: y = √x Domain-- Range-- Increasing/Decreasing

Examples: y = √x – 3 + 2 Graph the following square root equations: Domain-- Range-- Increasing/Decreasing

How do you recognize the various families? Cubic Family Equation: Graph: Pattern: y = a(x – h) 3 + k a = – (h,k) a = + (h,k) 1, 7

Examples: Graph the following cubic equations: y = x 3 Domain-- Range-- Increasing/Decreasing

Examples: Graph the following cubic equations: y = x 3 - 1 Domain-- Range-- Increasing/Decreasing?

Examples: Graph the following cubic equations: y = -(x-2) 3 + 4 Domain-- Range-- Increasing/Decreasing?

How do you recognize the various families? Cube Root Family Equation: Graph: Pattern: a = – a = + y = a 3 √x – h + k (h,k) 1, 7 y = a(x – h) 1/3 + k

Examples: y = 3 √x Graph the following cube root equations: Domain-- Range-- Increasing/Decreasing

Examples: y = 3 √x – 3 + 2 Graph the following cube root equations: Domain-- Range-- Increasing/Decreasing?

Identify the family of graphs for the following equations: EquationFamily 3x + 2y = 6 y = (x – 2) 2 + 1 y = | x – 4 | + 6 y = 3x 2 + 6x – 2 y = 2  x – 1 + 4 y = – 3  4 – x + 2 (x – 2) 2 + (y – 6) 2 = 4

Identify the family of graphs for the following equations: EquationFamily y = 2 / 3 | x – 4 | + 1 y =  1 – x x = 5 x 2 +y 2 + 3x -1 = 0 x 2 + y 2 = 84 y = – 3  x + 1 – 3 y = – 2

Identify the family of graphs for the following equations: EquationFamily y = – ( x – 4 ) 2 y = 2x 2 + 1 y = 3 / 2 x – 2 y = –2 | x | y = (x – 8) 1/3 - 3

 Average Rate of Change f(x 2 ) – f(x 1 ) x 2 - x 1 Change in y Change in x m sec

 A function y = f(x) is even if f(-x) = f(x)  A function y = f(x) is odd if f(-x) = -f(x)