9/18/ : Parent Functions1 Parent Functions Unit 1

9/18/ : Parent Functions2 What is a parent function? The parent function is the simplest function with the defining characteristics of the family. Functions in the same family are transformations of their parent function.

9/18/ : Parent Functions3 Algebra Aerobics

9/18/ : Parent Functions4 Types of Functions Family Rule Graph Domain Range Zeros Symmetry Linear f(x) = x All Real Numbers (–∞, ∞) All Real Numbers (–∞, ∞) Constant f(x) = c All Real Numbers (–∞, ∞) c None y-axis (0, 0) Origin

Family Rule Graph Domain Range Zeros Symmetry 9/18/ : Parent Functions5 Types of Functions Cubic f(x) = x 3 All Real Numbers (–∞, ∞) All Real Numbers (–∞, ∞) Quadratic f(x) = x 2 All Real Numbers (–∞, ∞) y > 0 [0, ∞) (0, 0) y-axis (0, 0) Origin

9/18/ : Parent Functions6 Types of Functions Cubic Root f(x) =. All Real Numbers (–∞, ∞) All Real Numbers (–∞, ∞) Square Root f(x) =. x > 0 [0, ∞) y > 0 [0, ∞) Family Rule Graph Domain Range Zeros Symmetry (0, 0) None (0, 0) Origin

9/18/ : Parent Functions7 Types of Functions Absolute Value f(x) = |x| All Real Numbers (–∞, ∞) y > 0 [0, ∞) Rational f(x) =. All Reals except 0 (–∞, 0), (0, –∞) All Reals except 0 (–∞, 0), (0, –∞) Family Rule Graph Domain Range Zeros Symmetry None Origin (0, 0) y-axis

9/18/ : Parent Functions8 Types of Functions Exponential f(x) = 2 x All Real Numbers (–∞, ∞) y > 0 [0, ∞) Logarithmic f(x) = log x x > 0 [0, ∞) All Real Numbers (–∞, ∞) Family Rule Graph Domain Range Zeros Symmetry None

9/18/ : Parent Functions9 Translations Show with your hands

9/18/ : Parent Functions10 f(x) = x – 3 Linear, Down 3

9/18/ : Parent Functions11 f(x) = x + 3 Linear, Up 3

9/18/ : Parent Functions12 f(x) = 2xf(x) = 2x Linear, Steeper by 2

9/18/ : Parent Functions13 f(x) = 2x 2 Shrinks with a scale of 2

9/18/ : Parent Functions14 f(x) = 2x 2 – 4 Quadratic Function, Shrinks scale of 2 and Down 4

9/18/ : Parent Functions15 f(x) = x Cubic, Up 2

9/18/ : Parent Functions16 f(x) = (–x) 2 Quadratic, Reflection

9/18/ : Parent Functions17 f(x) =. Square root, Shrinks by a scale of 3 and down by 4

9/18/ : Parent Functions18 Moves to the right by 2 and grows horizontally by a scale of 3

9/18/ : Parent Functions19 Parent Functions Examples Identify the parent function for g from its function rule. Then, describe what transformation of the parent function it represents. 1. g(x) = x – 3 2. g(x) = 2x 2 3. g(x) = x g(x) = (–x) 2 5. g(x) = 6. Linear, Down 3 Quadratic, Shrinks with a scale of 2 Cubic, Up 2 Quadratic, Reflection Square root, Shrinks by a scale of 3 and down by 4 Moves to the right by 2 and grows horizontally by a scale of 3

Parent Function Handout Work on Parent Function Handout Questions. This is a daily grade. 9/18/ : Parent Functions20