<span>Left & Right affect the h,
Up & Down affect the k,
Shrink & Stretch affect the "a" (which is in front of the absolute value expression).
1. shift 1 unit to the right and up 2 units → y = |x-1| + 2
2. </span><span>shift 3 units to the left and 7 units down → y = |x + 7| - 7
3. </span><span>vertical shrink by a factor of 1/3 → y =

|x|
4. </span><span>vertical stretch by a factor of 3
→ y = </span><span>3 |x|</span>
Answer:
The objective function in terms of one number, x is
S(x) = 4x + (12/x)
The values of x and y that minimum the sum are √3 and 4√3 respectively.
Step-by-step explanation:
Two positive numbers, x and y
x × y = 12
xy = 12
S(x,y) = 4x + y
We plan to minimize the sum subject to the constraint (xy = 12)
We can make y the subject of formula in the constraint equation
y = (12/x)
Substituting into the objective function,
S(x,y) = 4x + y
S(x) = 4x + (12/x)
We can then find the minimum.
At minimum point, (dS/dx) = 0 and (d²S/dx²) > 0
(dS/dx) = 4 - (12/x²) = 0
4 - (12/x²) = 0
(12/x²) = 4
4x² = 12
x = √3
y = 12/√3 = 4√3
To just check if this point is truly a minimum
(d²S/dx²) = (24/x³) = (8/√3) > 0 (minimum point)
Answer: x=2
step by step explanation:
1. 2.00/64=3.125 cents per oz
2. 7.50/256=2.930 cents per oz.
3. The best deal is at the whole sale