The table below shows the fifth powers of different numbers: Number (x) 1 −1 2 −2 Fifth power of the number (y) 1 −1 32 −32 Part A: Does the table represent y as a function of x? Justify your answer. (5 points) Part B: The total cost f(x), in dollars, for renting a bowling lane for x hours is shown below: f(x) = 2x + 12 What is the value of f(4) and what does f(4) represent? (5 points)
Accepted Solution
A:
Part A
Yes y is a function of x. Specifically the equation is y = x^5 For any given input, there is exactly one output
Notice how if x = 1 then y = x^5 = (1)^5 = 1 Notice how if x = -1 then y = x^5 = (-1)^5 = -1 Notice how if x = -2 then y = x^5 = (-2)^5 = -32 Notice how if x = 2 then y = x^5 = (2)^5 = 32
In general, x^5 = x*x*x*x*x there are five copies of x multiplied
A more specific example 3^5 = 3*3*3*3*3 there are five copies of '3' multiplied
All we do is replace x with 4 and use PEMDAS to simplify f(x) = 2x+12 f(4) = 2(4)+12 f(4) = 8+12 f(4) = 20
The value of f(4) is 20 What does it mean? It is the total cost of renting the bowling lane for 4 hours. If you rent it for four hours, then you'll pay a total of $20.
The portion 2x = 2*4 = 8 is the variable cost which depends on how long you play. The more hours, the more the variable cost goes up The fixed cost is 12. This is always fixed as this is the price to get in the door. If you play for 0 hours, but somehow got in the door, then you still pay $12 In total, variableCost+fixedCost = 8+12 = 20 = totalCost