QUIZ When done turn in the quiz to

QUIZ When done, turn in the quiz to the back and pick up a parent function chart and fill it out 6/18/2021 7: 44 AM Parent Functions 2

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PARENT FUNCTIONS Revised © 2014 Viet. dang@humble. k 12. tx. us 6/18/2021 7: 44 AM Parent Functions 4

WHAT IS A PARENT FUNCTION? A. 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. B. There are main parent functions that are utilized through Algebra. They are the following: 6/18/2021 7: 44 AM Parent Functions 5

PARENT FUNCTIONS Family Constant Linear Quadratic Cubic Rule f(x) = c f(x) = x 2 f(x) = x 3 Graph Table x – 2 – 1 0 1 2 y c c c y – 2 – 1 0 1 2 y 4 1 0 1 4 y – 8 – 1 0 1 8 Domain Range 6/18/2021 7: 44 AM Parent Functions 6

PARENT FUNCTIONS Family Square Root Cubic Root Reciprocal/Rational Absolute Value Exponential Rule f(x) = √x f(x) = 3√x f(x) = 1/x f(x) = |x| f(x) = 2 x Graph Table x 0 1 4 9 x – 8 – 1 0 1 8 x – 2 – 1 0 1 2 y 0 1 2 3 y – 2 – 1 0 1 2 y –. 5 – 1 D NE 1 . 5 y 2 1 0 1 2 y 1/4 1/2 1 2 4 Domain Range 6/18/2021 7: 44 AM Parent Functions 7

SCALE FACTOR (SCALAR) A. The equation will now look like, y = a(x – h) + k 1. _h_ stands for the Horizontal Shift 2. _k_ stands for the Vertical Shift B. The standard points will now be adjusted by the scalar (a) C. Multiply a with the x–values of the standard points. D. The scalar does not affect the new origin. 6/18/2021 7: 44 AM Parent Functions 8

VERTICAL SHIFTS OF A For shifts of A of ax 2 + bx + c = y, the bigger the A, the smaller the graph gets. 6/18/2021 7: 44 AM Parent Functions 9

VERTICAL SHIFTS OF C For shifts of C of ax 2 + bx + c = y, the change of the C, the y– intercept shifts up or down 6/18/2021 7: 44 AM Parent Functions 10

HORIZONTAL SHIFTS For shifts of A of f(x)= a(x – h)2 + k, the change of the h, the graph shifts either left or right If the equation is… ADDED, it moves to the LEFT SUBTRACTED, it moves to the RIGHT 6/18/2021 7: 44 AM Parent Functions 11

REFLECTION SHIFTS For horizontal shifts of f(x)= –a(x – h)2 + k or others, the change of the a, the graph shifts reflects on the axis 6/18/2021 7: 44 AM Parent Functions 12

LET’S DANCE 6/18/2021 7: 44 AM Parent Functions 13

AEROBIC MOVES 6/18/2021 7: 44 AM Parent Functions 14

EXAMPLE 1 Given the graph of f(x) = x – 3, determine the domain, range, and transformation change in Interval Notation 6/18/2021 7: 44 AM Parent Functions 15

EXAMPLE 2 Given the graph of f(x) = 2 x, determine the domain, range, and transformation change in Interval Notation 6/18/2021 7: 44 AM Parent Functions 16

YOUR TURN Given the graph of f(x) = (1/2)x + 5, determine the domain, range, and transformation change in Interval Notation 6/18/2021 7: 44 AM Parent Functions 17

EXAMPLE 3 Given the graph of f(x) = (x + 1)2 – 3, determine the domain, range, and transformation change in Interval Notation 6/18/2021 7: 44 AM Parent Functions 18

EXAMPLE 4 Given the graph of f(x) = –|x – 2| + 4, determine the domain, range, and transformation change in Interval Notation 6/18/2021 7: 44 AM Parent Functions 19

EXAMPLE 5 Given the graph of f(x) = y = – 2(x – 3)3 + 1, determine the domain, range, and transformation change in Interval Notation 6/18/2021 7: 44 AM Parent Functions 20

YOUR TURN Given the graph of f(x) = (x – 1)2 – 4, determine the domain, range, and transformation change in Interval Notation 6/18/2021 7: 44 AM Parent Functions 21

EXAMPLE 6 Given a linear parent function, the shift of the equation is 4 units up, determine the equation. 6/18/2021 7: 44 AM Parent Functions 22

EXAMPLE 7 Given an absolute value parent function, the shift of the equation is 4 units down and 2 units to the left, determine the equation. 6/18/2021 7: 44 AM Parent Functions 23

YOUR TURN Given a quadratic parent function, the shift of the equation is 3 units down and 4 units to the left, determine the equation. 6/18/2021 7: 44 AM Parent Functions 24

ASSIGNMENT Worksheet 6/18/2021 7: 44 AM Parent Functions 25