University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

233

Pages:

6
Author:

albulaastediasjn4

Ch 5 Study Guide Content: 5.1 1) (9x⁴)^(1/2) = √(9x⁴) = 3x² 2) 32^(5/2) = (√32)^5 = (2^5)^2 = 2^10 = 1024 3) x^(2/3) + 1 = 65 x^(2/3) = 64 (x^(2/3))^(3/2) = (64)^(3/2) x = (√64)^3 x = (8)^3 x = 512 4) x^(2/3) + 2 = 10 x^(2/3) = 8 (x^(2/3))^(3/2) = (8)^(3/2) x = (√8)^2 x = (2)^2 x = 4 5.2 1) 5√(4/128) = 5√(1/32) = 5√(1)/5√(32) = 1/2 2) (8³ * 8^(-1/2))^(-2) = (8^(5/2))^(-2) = 8^(-5) = 1/8⁵ 3) √(12 * √8) = √(12 * √(42)) = √(12 * 2√2) = √(24√2) = √(16√6) = 4√(√6) = 4√(√6) 4) 6/(4-√3) * (4+√3)/(4+√3) = (24+6√3)/(4^2-(√3)^2) = (24+6√3)/(16-3) = (24+6√3)/13 5) √[3]81 + 15√[3]3 = √[3](27 * 3) + 15√[3]3 = 3√[3]3 + 15√[3]3 = 18√[3]3 5.3 1) f(x) = √[3]x g(x) = 2√[3]x-5 + 3 Translation right 5 and up 3 and a vertical stretch by a factor of 2 A graph is shown with f(x) and g(x) labeled. 2) g(x) = -√[4]x + 2 A graph is shown with g(x) labeled. A point (-2, 3) is marked on the graph. 3) y = 1/2√x+2 - 3 vertical shrink Domain: x ≥ -2 Range: y ≥ -3 A graph is shown with the parent function √x labeled. A point (-2, -3) is marked on the graph. Certainly, here's the analysis of the image you provided: Content: 5.4 Problem: √(x + 24) = (x + 12) Solution: x + 24 = (x + 12)(x + 12) x + 24 = x² + 24x + 144 0 = x² + 23x + 120 0 = (x + 15)(x + 8) x = -15 (Extraneous) x = -8 Problem: (√(4x - 4))² = (-1 + √(5x - 1))² Solution: 4x - 4 = (-1 + √(5x - 1))(-1 + √(5x - 1)) 4x - 4 = -2√(5x - 1) + 5x - 1 -x - 3 = -2√(5x - 1) (-x - 3)² = (√(5x - 1))² (x + 3)² = 5x - 1 (x + 3)(x + 3) = 5x - 1 x² + 8x + 16 = 5x - 1 x² + 3x + 17 = 0 (x - 10)(x - 2) = 0 x = 10 x = 2