University:
Florida Gateway College
Course:
MAT 0028 | Elementary Algebra
Academic year:

2019
Views:

367

Pages:

3
Author:

5CelestialChronicle

Algebra 2 Honors Rationals Quiz 2 Review 1. A pharmacist wishes to make 1.8 L of a 10% solution of boric acid by mixing 7.5% and 12% solutions. How much of each type of solution should be used? 7.5% 12% 10% L L L x 1.8-x 1.8 0.075x + 0.12(1.8-x) = 0.1(1.8) 0.075x + 0.216 - 0.12x = 0.18 -0.045x = -0.036 x = 0.8 L 0.8 L of 7.5% 1.0 L of 12% 2. Pipes A and B can fill a storage tank in 8 h and 12 h respectively. With the tank empty, pipe A was turned on at noon and then pipe B was turned on at 1:30 PM. At what time did the tank fill? Rate Time Total A 8 t B 12 t-1.5 (1/8)t + (1/12)(t-1.5) = 1 3t + 2t - 3 = 24 5t = 27 t = 27/5 = 5.4 hours 5 hours 24 min Filled @ 5:24 pm 3. An excursion boat traveled 35 km upstream and then back again in 4 h 48 min. If the speed of the boat in still water is 15 km/h, what is the speed of the current? Rate Time Dist Up 15-x 35 Down 15+x 35 35/(15-x) + 35/(15+x) = 4.8 525+35x+525-35x = 1080-4.8x² 4.8x² - 30 = 0 x² = 6.25 x = 2.5 km/h State the vertical and horizontal asymptotes. f(x) = 2x/(x-3) VA: x = 3 HA: y = 2 g(x) = (x-5)/(x²-2x-24) = (x-5)/((x-6)(x+4)) VA: x = 6, -4 HA: y = 0 6. Graph the functions f(x) = (x-3)/(x+2). Find a) horizontal and vertical asymptotes, b) x- and y-intercepts, and c) domain and range. Be sure to include End Behavior Sentences. VA: x = -2 HA: y = 1 x-int: 0 = x - 3; x = 3 (3, 0) y-int: y = -3/2; (0, -3/2) D: (-∞, -2) U (-2, ∞) R: (-∞, 1) U (1, ∞) As x -> ∞, f(x) -> 1 As x -> -∞, f(x) -> 1 7. Graph the functions f(x) = (2x-5)/(x-2). Find a) horizontal and vertical asymptotes, b) x- and y-intercepts, and c) domain and range. Be sure to include End Behavior Sentences. VA: x = 2 HA: y = 2 x-int: 2x - 5 = 0; x = 5/2 (5/2, 0) y-int: y = -5/2; (0, -5/2) D: (-∞, 2) U (2, ∞) R: (-∞, 2) U (2, ∞) As x -> ∞, f(x) -> 2 As x -> -∞, f(x) -> 2 8. Graph the functions f(x) = 2x/(x²-4). Find a) horizontal and vertical asymptotes, b) x- and y-intercepts, and c) domain and range. Be sure to include End Behavior Sentences. VA: x = ±2 HA: y = 0 x-int: 2x = 0; (0, 0) y-int: y = 0/(-4); (0, 0) D: (-∞, -2) U (-2, 2) U (2, ∞) R: (-∞, ∞) As x -> ∞, f(x) -> 0 As x -> -∞, f(x) -> 0 9. Graph the functions f(x) = x²/(x²-9). Find a) horizontal and vertical asymptotes, b) x- and y-intercepts, and c) domain and range. Be sure to include End Behavior Sentences. VA: x = ±3 HA: y = 1 x-int: 0 = x²; (0, 0) y-int: y = 0/-9; (0, 0) D: (-∞, -3) U (-3, 3) U (3, ∞) R: (-∞, 0] U (1, ∞) As x -> ±∞, f(x) -> 1 Answers 0.8 L of 7.5% and 1.0 L of 12% 5:24 pm 2.5 km/h VA: x = 3; HA: y = 2 VA: x = 6, -4; HA: y = 0 VA: x = -2; HA: y = -1; x-int: (3, 0); y-int: (0, -3/2); D: (-∞, -2) U (-2, ∞); R: (-∞, -1) U (1, ∞); As x -> ±∞, f(x) -> -1 VA: x = 3; HA: y = 2; x-int: (5/2, 0); y-int: (0, -5/2); D: (-∞, 3) U (3, ∞); R: (-∞, 2) U (2, ∞); As x -> ±∞, f(x) -> 2 VA: x = ±2; HA: y = 0; x-int: (0, 0); y-int: (0, 0); D: (-∞, -2) U (-2, 2) U (2, ∞); R: (-∞, ∞); As x -> ±∞, f(x) -> 0 VA: x = ±3; HA: y = 1; x-int: (0, 0); y-int: (0, 0); D: (-∞, -3) U (-3, 3) U (3, ∞); R: (-∞, 0] U (1, ∞); As x -> ±∞, f(x) -> 1

Math Algebra Rational Quiz 2 Review Key

Related Documents

Recommended Documents

Description

Related Documents

Free up your schedule!

Take 5 seconds to unlock