8.1 and 8.2 Inverse and Direct Variation
1. Assume k is a constant of variation, write an equation that represents a situation in which y varies inversely with x when: x = 5 y = 2
y = 10/x
8. Find the domain of the rational function: y= 2/(x+1)
D: all real numbers except x=-1
Simplify the rational expression: (9x12y7z)/(36x15y3z2)
What is y4/(4x3z)
Find the least common multiple of the pair of polynomials: 4x2+12x+9 and 4x2-9
(2x+3)2(2x-3)
Solve the equation. Check each solution: x/3 + x/2 =10
x = 12
3. Assume k is a constant of variation, write an equation that represents a situation in which y varies inversely with x when: x = 2/3 y = 4/5
y = 8/(15x)
9. Find the vertical asymptotes and holes for the graph of the rational function: y= (x+3)/(x2-9)
vertical asymptote at x = 3; hole at x = -3
Simplify the rational expression. State any restrictions on the variables: (4x+6)/(2x+3)
2 ; x≠ -1.5
Simplify the sum. State any restrictions on the variables: (6y-4)/(y2-5) + (3y+1)/(y2-5)
3(3y-1)/(y2-5) ; y≠ sq. rt. 5 , - sq. rt. 5
Solve the equation. Check each solution: 3x/4 = 5x+1/3
x = -4/11
4. Assume k is a constant of variation, write an equation that represents a situation in which z varies jointly with y and inversely with x when: x = 5 y = 2 z = 10
z = (25y)/x
10. Find the domain, points of discontinuity, and x- and y-intercept: y= (x-3)(x+1)/(x-2)
D:all real numbers except x=2;x=2 non-removable; (-1, 0) (3, 0), (0, 1.5)
Multiply. State any restrictions on the variables:(2x+4)/(10x) X (15x2)/(x+2)
3x; x ≠ 0, -2
Simplify the difference. State any restrictions on the variables: 3/(8x3y3) - 1/4xy
(3 - 2x2y2)/(8x3y3); x≠ 0,y≠ 0
Solve the equation. Check each solution: 2y/5 + 2/6 = y/2 - 1/6
x = 5
6. Assume k is a constant of variation, write an equation that represents a situation in which z varies jointly with y and inversely with x when: x = 2/3 y = 3/2 z = 4/5
y = (5y)/(4x)
11. Find the domain, points of discontinuity (mention their type), x- and y-intercepts of the rational function: 4x/x4+16
D: all real numbers; none; (0, 0)
Divide. State any restrictions on the variables: (7x4)/(24y5) ÷ (21x)/(12y4)
x3/6y; y≠ 0
Find the least common multiple of the pair of polynomials: 2x2-18 and 5x3+30x2+45x
10x(x+3)2(x-3)
Solve the equation. Check each solution: 1/(2x+2) + 5/(x2-1) = 1/(x-1)
x = 7
7. A farmer pumps water from an irrigation well to water his field. The time it takes to water the field varies inversely with the rate at which the pump operates. It takes 10 hours to water the field when the pumping rate is 300 gallons per minute. If he adjusts the pumping rate to 800 gallons per minute, how long will it take to water the field?
3.75 hours
Find the domain, points of discontinuity, x- and y-intercepts, and horizontal asymptote of the rational function: y=1/(x2+2x-8)
D: all real numbers except x = 2 and x = -4; non-removable point of discontinuity at x = 2 and removable point of discontinuity at x = -4; x-intercept: none; y-intercept: y = -0.5; Horizontal asymptote: y=0
Divide. State any restrictions on the variables: (x2-4)/(x2+6x+9) ÷ (x2+4x+4)/(x2-9)
(x2-5x+6)/(x2+5x+6); x≠ -2,-3,3
Simplify the complex fraction: (5/(x+3))/(2+(1/x+3))
5/(2x+7)
Solve the equation. Check each solution: 2/(x+3) + 5/(3-x) = 6/(x2-9)
x = -9