Answer:
11. ×8; ×27; ÷8
12. ÷16; ÷256; ×16
13. ×8
14. ×4
Step-by-step explanation:
11. g(x) =5x³
g₁ = 5x₁³
g₂ = 5x₂³
g₂/g₁ = (x₂/x₁)³
a. x is doubled. g₂/g₁ = (2x₁/x₁)³ = 2³ = 8
If x is doubled, g is multiplied by eight.
b. If x is tripled, g₂/g₁ = (3x₁/x₁)³ = 3³ = 27
If x is tripled, g is multiplied by 27.
c. If x is halved, g₂/g₁ = (½x₁/x₁)³ = (½)³ = ⅛
If x is halved, g is divided by 8.
12. ƒ(x) = 3/x⁴
f₁ = 1/x₁⁴
f₂ = 1/x₂⁴
f₂/f₁ = (x₁/x₂)⁴
a. x is doubled. f₂/f₁ = (x₁/2x₁)⁴ = (½)⁴ = 1/16
If x is doubled, f is divided by 16.
b. If x is quadrupled, f₂/f₁ = (x₁/4x₁)⁴= (¼)⁴ = 1/256
If x is tripled, f is divided by 256.
c. If x is halved, f₂/f₁ = [x₁/(½x₁)]⁴ = 2⁴ = 16
If x is halved, f is multiplied by 16.
13. V = ⁴/₃πr³
V₁ = ⁴/₃πr₁³
V₂ = ⁴/₃πr₂³
V₂/V₁ = (r₂/r₁)³
r is doubled. V₂/V₁ = (2r₁/r₁)³ = 2³ = 8
The volume of the sphere is multiplied by 8.
14. V = πr²h
V₁ = πr₁²h
V₂ = πr₂²h
If r is doubled and h stays the same, V₂/V₁ = (2r₁/r₁)² = 2² = 4
The volume of the cylinder is quadrupled.
