Question

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

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?

Answer 1

Part A
When x=1, x⁴ = 1⁴ = 1
Because y = 1, x⁴ = y.
When x=2, x⁴ = 2⁴ = 16
Because y = 16, x⁴ = y

y = x⁴ according to the given table.
For each given x, there is only one value of y, so it is a function.

Answer: The table represents a function of x.

Part B
f(x) = 17x + 50
where
x = hours to rent a truck
f(x) = cost in dollars

When x = 30 hours, f(30) = 17*30 + 50 = $560

Answer:
f(30) represents the cost in dollars to rent a truck for 30 hours.
The value of f(30) is $560.