Unit 1 A Day 1 Parent Function Characteristics

Unit 1 A Day 1: Parent Function Characteristics • As you come in, write down your learning target(s): • Describe critical attributes of a function including: domain and range using interval and set notation • Describe if a function is increasing, decreasing, or is constant over a specific interval • Determine local and absolute maximums and minimums • Describe the end behaviors of the function • • Brief Introductions Card Match Activity Parent Function Characteristics Discussion Homework due next class: Transformation Review, Review and Check List Items for Thurs/Fri & Complete Notes High Level Questions & Summary

Introductions & Class Procedures

Card Matching Activity

Warm-up • Determine the domain and range of the following function in set and interval notations.

Pre-Calculus Parent Functions and their Characteristics

Parent Functions from Algebra II Constant (Horizontal Line) Linear (Identity) Absolute Value Quadratic Square Root Cube Root Rational Exponential Logarithmic

Additional Parent Functions in Pre-cal • Cubic • Sine • Cosine • Step (Greatest Integer Function) • Logistic

Parent Functions Characteristics from Algebra II • Equation • Graph • Table • Domain • Range • Horizontal Asymptote • Vertical Asymptote

Parent Functions Characteristics from Algebra II – Equation, Graph, & Table My requirements: • When writing the equation for a parent function: • use function notation (f(x), g(x), etc. ) instead of y =. • When graphing, label all key characteristics for the function • For example: vertex, min/max, asymptotes, line of symmetry, etc. • When selecting points for the table or graph: • Provide/graph at least 7 points; some negative and some positive

Parent Functions Characteristics from Algebra II – Domain & Range

Parent Functions Characteristics from Algebra II – Asymptotes • The line (force field) that your function converges towards… • Horizontal: • y = lower or upper boundary as x approaches -∞ or +∞ • Vertical: • x = left or right boundary as y approaches -∞ or +∞

Additional Parent Functions Characteristics in Pre-Calculus • Axis of Symmetry & Point of Symmetry • End Behavior • Continuity • Increasing/Decreasing • Absolute Extreme • Local Extreme(s)

Additional Parent Functions Characteristics in Pre-Calculus: Line of Symmetry Axis of Symmetry & Point of Symmetry: • Symmetric to the y-axis (x, y) (-x, y) • Symmetric to the x-axis (x, y) (x, -y) • Symmetric to the origin (x, y) (-x, -y) In this first unit we will also determine if a function’s symmetry is odd, even or neither both graphically and algebraically: Even: Symmetrical about the y axis (folds over y axis). Odd: Symmetrical about the origin (flips over x axis and folds over y axis or 180 degree rotation around the origin). Neither: Not Symmetrical.

Additional Parent Functions Characteristics in Pre-Calculus: End Behavior As x approaches -∞ or ∞ what does y approach or end at? (Left end, Right end) x -∞ y = ∞ , x ∞ y= - ∞ x -6 y = -∞ , x 5 y = ∞ x -∞ y = -∞ , x ∞ y= 3

Additional Parent Functions Characteristics in Pre-Calculus: Continuity/Discontinuity • Are there any breaks in the function? Yes: Discontinuous No: Continuous

Additional Characteristics: Increasing/Decreasing: What does y do as x increases or decreases? Increasing: Decreasing: Constant: as x increases y decreases y is constant

Additional Parent Functions Characteristics in Pre-Calculus: Extrema • Extrema: The minimum and maximum points on a graph including the end points. • End points: Ends of graph & where the graph turns from increasing to decreasing and vice-versa. • Local (Relative) Extrema: Every turn in the graph. • Absolute (Global) Extrema: The “absolute” highest or lowest point of the graph. • Boundedness: (May or May not be caused by a horizontal asymptote) • Bounded Above: Has an absolute maximum • Bounded Below: Has an absolute minimum • Bounded: Has both an absolute maximum and minimum

Additional Parent Functions Characteristics in Pre-Calculus: Extrema Examples with bounds: Not Bounded (Local min/max) Bounded (above/below) (Local min and max (Note: There arrows on both ends) Bounded above (Local min/max, absolute max) Bounded below (Local/Absolute Min)

Transformations Review (Homework) • Each teacher needs to create the handout with their own links and paste that here.

Homework • Transformation Review • Review and Check List Items for Thurs/Fri • Complete Notes High Level Questions & Summary