University:
College Entrance Preparation
Course:
ACT Preparation (Mathematics)
Academic year:

2024
Views:

55

Pages:

2
Author:

palangresq3v

**Name:** **Date:** **Period:** **Key** Identify the points of discontinuity, holes, vertical asymptotes, x-intercepts, and horizontal asymptote of each. 1. f(x) = 1 / (3x² + 3x - 18) = 1 / (3(x+3)(x-2)) VA: x = -3, x = 2 Holes: None HA: y = 0 x-int: None y-int: y = -1/18 2. f(x) = (x-4)/(x-4) VA: None Holes: x = 4 HA: y = 1 x-int: None y-int: y = 1 3. f(x) = (x²-x-6)/(-3x²-3x+18) = (x(x-3)(x+2))/(-3(x+3)(x-2)) VA: x = -3, x = 2 Holes: x = -3 HA: y = -1/3 x-int: x = 2 y-int: y = 1/3 4. f(x) = (x²+x-6)/(-4x²-16x-12) = ((x+3)(x-2))/(-4(x+3)(x+1)) VA: x = -4 Holes: x = -3 HA: y = -1/4 x-int: x = 2 y-int: y = 1/2 Identify the points of discontinuity, holes, vertical asymptotes, and horizontal asymptote of each. Then sketch the graph. 5. 1 f(x) = 4/x VA: x = 0 Holes: None HA: y = 0 x-int: None y-int: None [Image of a graph of f(x) = 4/x] 6. f(x) = -4/x VA: x = 0 Holes: None HA: y = 0 x-int: None y-int: None [Image of a graph of f(x) = -4/x] 7. f(x) = (x+4)/(-2x-6) = (x+4)/(-2(x+3)) VA: x = -3 Holes: None HA: y = -1/2 x-int: x = -4 y-int: y = 2/3 [Image of a graph of f(x) = (x+4)/(-2x-6)] 8. f(x) = (x²-9)/(3x²-6x-9) = (x-3)(x+3)/(3(x-3)(x+1)) VA: x = -1 Holes: x = 3 HA: y = 1/3 x-int: x = -3 y-int: y = 1 [Image of a graph of f(x) = (x²-9)/(3x²-6x-9)] 9) f(x) = (3x²-12) / (x²-3) = 3(x+2)(x-2) / (x+√3)(x-√3) VA: x = ±√3 Holes: None HA: y = 3 x-int: x = ±2 y-int: y = 0 [Image of a graph of f(x) = (3x²-12) / (x²-3)] 10) f(x) = (x² + 16x + 24) / (x² - 4x - 32) = (x+3)(x+8) / (x-8)(x+4) VA: x = 8, x = -4 Holes: None HA: y = 1 x-int: x = -3, x = -8 y-int: y = -3/4 [Image of a graph of f(x) = (x² + 16x + 24) / (x² - 4x - 32)] 11) f(x) = (2x² - 4x) / (4x + 8) = x(x-2) / 4(x+2) VA: x = -2 Holes: None HA: None x-int: x = 0, x = 2 y-int: y = 0 [Image of a graph of f(x) = (2x² - 4x) / (4x + 8)] 12) f(x) = (x² + 2x - 6) / (2x + 6) VA: x = -3 Holes: None HA: None x-int: x ≈ -3.73, x ≈ 1.63 y-int: y = -1 [Image of a graph of f(x) = (x² + 2x - 6) / (2x + 6)] 13) f(x) = (2x² + 10x + 12) / (3x² + 10x + 2) = 2(x+3)(x+2) / (3x+1)(x+2) VA: x = -1/3 Holes: x = -2 HA: y = 2/3 x-int: x = -3 y-int: y = 6 [Image of a graph of f(x) = (2x² + 10x + 12) / (3x² + 10x + 2)] 14) f(x) = 3 / (x - 2) VA: x = 2 Holes: None HA: y = 0 x-int: None y-int: y = -3/2 [Image of a graph of f(x) = 3 / (x - 2)]