Practice Questins Answers | High School

University:
High School
Course:
High School Algebra
Academic year:

2022
Views:

110

Pages:

5
Author:

Omari Mccormick

Alg 2/Trig: Ch1 Practice Worksheet 1. h(x) = |x| + 3 Parent is absolute value: y = |x| Vertical translation 3 units up Domain: All R Range: y ≥ 3 2. g(x) = (x - 4)^2 Parent is quadratic: y = x^2 Horizontal translation 4 units right Domain: All R Range: y ≥ 0 3. p(x) = x + 3 Parent is linear: y = x Vertical translation 3 units up Domain: All R Range: All R 4. g(x) = -(9x - 2) Reflected x-axis g(x) = -f(x) g(x) = -(9x - 2) g(x) = -9x + 2 Reflected y-axis g(x) = f(-x) g(x) = 9(-x) - 2 g(x) = -9x - 2 Vertical Shrink of 3 g(x) = a f(x) g(x) = (9x - 2)/3 g(x) = 3x - 2/3 5. f(x) = 9x - 2 a) 4 units up g(x) = f(x) + k g(x) = 9x - 2 + 4 g(x) = 9x + 2 b) 2 units right g(x) = f(x - h) g(x) = 9(x - 2) - 2 g(x) = 9x - 18 - 2 g(x) = 9x - 20 Target 1C Problem 6 Points: (0,0) and (5,24) Slope: m = (24-0)/(5-0) = 24/5 miles/second or 4.8 miles/second Equation: y = 24/5x or y = 4.8x Calculation: 17200 = 24/5x Result: x = 3583.3 seconds or ~59.7 minutes Problem 7 Points: (0,18) and (10,15) Slope: m = (18-15)/(0-10) = -0.3 (thousands)/payment or $300/payment Equation: y = -0.3x + 18 or y = -3/10x + 18 Calculation: y = 0.3(36) + 18 = 28.8 (thousands) Result: After 36 payments, the balance is $7,200. Calculations: Slope: m = (1800 - 1500) / (125 - 100) = 300 / 25 = 12 $12/student Y-intercept: y - y1 = m(x - x1) Use (100, 1500) y - 1500 = 12(x - 100) y - 1500 = 12x - 1200 y = 12x + 300 Interpretation: Lakeside: $12/student + $300 fee Sunview: $10/student + $600 fee Comparison: Sunview charges $10/student, which is $2 less than Lakeside. Equation Setting: Let equations = each other 12x + 300 = 10x + 600 12x - 300 = 10x 2x = 300 x = 150 Conclusion: 150 students must attend for the costs to be the same. Problem 7 Equations: 2x - 3y + z = 10 (EA) -x + 2y + z = 5 (EB) 3x + 2y - z = 7 (EC) Eliminate x: (EA) + (EB) x - 6y - 2z = -8 (ED) Eliminate x: (EC) + 3(EB) 5x + 8y = 26 (EF) Eliminate y: 8(ED) + (EF) 2z = -54 z = -27 Substitute z = -27 into (ED): -y + z = -6 -y - 27 = -6 -y = 21 y = -21 Substitute z = -27, y = -21 into (EA): 2x - 3(-21) + (-27) = 10 2x + 63 - 27 = 10 2x + 36 = 10 2x = -26 x = -13 Solution: (-13, -21, -27) Problem 8 Equations: x - 2y + z = 8 (EA) -x + 5y + 3z = 2 (EB) 3x + 2y - 4z = 18 (EC) Eliminate x: (EA) + (EB) 3y + 4z = 10 (ED) Eliminate x: 3(EA) + (EC) 11y + z = 42 (EF) Eliminate y: 11(ED) - (EF) 43z = 182 z = 4 Substitute z = 4 into (ED): 3y + 4(4) = 10 3y + 16 = 10 3y = -6 y = -2 Substitute z = 4, y = -2 into (EA): x - 2(-2) + 4 = 8 x + 4 + 4 = 8 x + 8 = 8 x = 0 Solution: (0, -2, 4) Problem 9 Equations: x - 2y + z = 11 (EA) -x + 5y + 3z = 2 (EB) 3x + 2y - 4z = 7 (EC) Eliminate x: (EA) + (EB) 3y + 4z = 13 (ED) Eliminate x: (EC) + 3(EB) 17y + 5z = 13 (EF) Eliminate y: 17(ED) - 3(EF) 43z = 182 z = 4 Substitute z = 4 into (ED): 3y + 4(4) = 13 3y + 16 = 13 3y = -3 y = -1 Substitute z = 4, y = -1 into (EA): x - 2(-1) + 4 = 11 x + 2 + 4 = 11 x + 6 = 11 x = 5 Solution: (5, -1, 4) Problem 10 Equations: x - 2y + z = 11 (EA) -x + 5y + 3z = 2 (EB) 3x + 2y - 4z = 7 (EC) Eliminate x: (EA) + (EB) 3y + 4z = 13 (ED) Eliminate x: (EC) + 3(EB) 17y + 5z = 13 (EF) Eliminate y: 17(ED) - 3(EF) 43z = 182 z = 4 Substitute z = 4 into (ED): 3y + 4(4) = 13 3y + 16 = 13 3y = -3 y = -1 Substitute z = 4, y = -1 into (EA): x - 2(-1) + 4 = 11 x + 2 + 4 = 11 x + 6 = 11 x = 5 Solution: (5, -1, 4)