2.02 ExpLog - Exponential Graphing and Properties

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

2024
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12
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2.02 GRAPHING Exponential Functions 𝑏 𝑥−ℎ If 𝑓 𝑥 = 𝑎𝑐 +𝑘 use exponent rules to simplify: Simplified Standard Form 𝑓 𝑥 = 𝑎𝑐 𝑏 𝑥−ℎ +𝑘 𝑓 𝑥 = 𝑎𝑐 𝑏𝑥−𝑏ℎ + 𝑘 𝑐 𝑏𝑥 𝑓 𝑥 = 𝑎 𝑏ℎ + 𝑘 𝑐 𝑎 𝑏𝑥 𝑓 𝑥 = ( 𝑏ℎ )𝑐 + 𝑘 𝑐 𝑎 𝑓 𝑥 = ( 𝑏ℎ )(𝑐 𝑏 )𝑥 + 𝑘 𝑐 Simplified Standard Form 𝑓 𝑥 = 𝑥 𝑎𝑐 +𝑘 Will use for rule-finding, use either form for graphing. Simplified Standard Form • Ex: Convert f x = −4 2 simplified standard form. • 𝑓 𝑥 = −4 2 2𝑥−2 −7 • 𝑓 𝑥 = −4 2 2𝑥 −2 • 𝑓 𝑥 = −4 • 2 2 𝑥 1 2 4 • 𝑓 𝑥 =− 4 𝑥 2 𝑥−1 − 7 to −7 −7 −7 Conversion to Simplified Standard • Plot horizontal asymptote 𝑦 = 𝑘 • Use Rule 𝑥, 𝑦 ⟼ 𝑥 𝑏 + ℎ, 𝑎𝑦 + 𝑘 BASIC ORDERED PAIRS ⟼ TRANSFORMED 1 −1, ⟼ (___) 𝑐 0,1 ⟼ (___) 1, 𝑐 ⟼ (___) • Plot transformed BOP To Sketch Graph • 𝑓 𝑥 = −3 2 − 𝑥−1 +5 𝑎 = −3, 𝑏 = −1, 𝑐 = 2, ℎ = 1, 𝑘 = 5 • Use Rule 𝑥, 𝑦 ⟼ −𝑥 + 1, −3𝑦 + 5 BASIC ORDERED PAIRS ⟼ TRANSFORMED 1 7 −1, ⟼ 2, 2 2 0,1 ⟼ (1, 2) 1, 2 ⟼ (0, −1) Try It… • 𝑓 𝑥 = −3 2 − 𝑥−1 + 5 • Graph the Points: Try It… • 𝑓 𝑥 = −3 2 − 𝑥−1 • 𝑓 𝑥 = −3 1 2 • 𝑓 𝑥 = −3 1 𝑥 (2) 1 (2) • 𝑓 𝑥 = −6 𝑥−1 +5 +5 +5 1 𝑥 2 +5 • 𝑎 = −6, 𝑏 = 1, 𝑐 = 1/2, ℎ = 0, 𝑘 = 5 Also simplified standard… 0<𝑐<1 𝑐>1 Visions 1 P173: #1, #2a #3bdf (convert to standard simplified form) Homework