1.02A - Square Root Intro and Basic Function

University:
High School
Course:
High School Physics
Academic year:

2024
Views:

255

Pages:

17
Author:

1 1

SQUARE ROOT FUNCTIONS SQUARE ROOT FUNCTIONS 1.02A – CONCEPT & BASIC FUNCTION There are two square roots for any positive real number 𝑎 The positive square root is written 𝑎 The negative square root is written − 𝑎 The Concept 1. ( 𝑎)2 = 𝑎⋅ 𝑎 =𝑎 Law of Square Roots 2. 𝑎⋅ 𝑏 = 𝑎𝑏 Law of Square Roots 3. 𝑎 𝑏 = 𝑎 𝑏 Law of Square Roots • We have also seen that: 4. 𝑎 𝑥 + 𝑏 𝑥 = (𝑎 + 𝑏) 𝑥 5. 𝑎 𝑥 − 𝑏 𝑥 = 𝑎 − 𝑏 Law of Square Roots 𝑥 • We have also seen that: 6. 𝑎 𝑏 ⋅ 𝑏 𝑏 = 𝑎𝑏 𝑏 This is rationalizing the denominator! 7. 1 𝑎+ 𝑏 ⋅ 𝑎− 𝑏 𝑎− 𝑏 = 𝑎− 𝑏 𝑎−𝑏 Law of Square Roots 1. 162 2. 5 10 × 8 5 × 2 6 Examples =9 2 = 800 3 3. −4 216 + 3 96 4. 3 3−2 7 2 3+ 7 Examples = −12 6 = 4 − 21 5. −45 42 15 6 6. 3 7−5 7 Examples = −3 7 = 21−5 7 7 7. 4 7−2 3 7+3 3 Examples −23 + 7 21 = 10 • As a concept … 𝑦=± 𝑥 • For a function, choose only the positive square root: keeping both makes a relation. 𝑎𝑛𝑦𝑡ℎ𝑖𝑛𝑔 2 ≠ 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒‼ REMEMBER 𝑓 𝑥 = 𝑥, 𝑥≥0 Domain is restricted! The Basic Square Root Function • • • • • • • 𝑑𝑜𝑚 𝑓 = ℝ+ 𝑟𝑎𝑛 𝑓 = ℝ+ 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 = 0 𝑧𝑒𝑟𝑜 = 0 min 𝑓 = 0 max 𝑓 = 𝐷𝑁𝐸 Variation • 𝑠𝑡𝑟𝑖𝑐𝑡𝑙𝑦 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑖𝑛𝑔 𝑜𝑣𝑒𝑟 ℝ+ • Sign • 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑜𝑣𝑒𝑟ℝ+ • 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝑓𝑜𝑟 𝑥 = 0 • Vertex = (0, 0) • Basic Ordered Pairs • { 0, 0 , 1, 1 , 4, 2 , (9, 3)} The Basic Properties •P39 #1, 2, 3 Homework