The table below shows the fourth powers of different numbers:
Number (x) 1 -1 2 -2
Fourth Power of the number (y) 1 1 16 16
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 truck for x hours is shown below:
f(x) = 17x + 50
What is the value of f(30) and what does f(30) represent? (5 points)
A) y does represent a function of x, as in the equation y=f(x)=x^4
B) If f(x)=17x+50, then f(30)=17(30)+50=560. f(30) represents the cost of renting a truck for 30 hours.
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Part A: To determine if the table represents y as a function of x, we need to check if each value of x has exactly one corresponding value of y.
Looking at the table, for each value of x, there is only one corresponding value of y. For example, for x=1, y=1. For x=-1, y=1. For x=2, y=16, and for x=-2, y=16.
Since each value of x has exactly one corresponding value of y, the table represents y as a function of x.
Part B: The given equation represents the total cost f(x) in dollars for renting a truck for x hours, where f(x) = 17x + 50.
To find the value of f(30), we substitute 30 in place of x in the equation:
f(30) = 17 * 30 + 50
= 510 + 50
= 560
Therefore, f(30) is equal to 560.
Similarly, we can interpret what f(30) represents. In this context, f(30) represents the total cost, in dollars, for renting a truck for 30 hours.