Question

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?

Answer 1

To answer Part A of the question, we don't have to do any math, merely just look at the table. We also have to understand how to represent y as a function of x. When y is represented as a function of x, that means there is a singular specific y value for each x value. Now looking at the graph, we can see this is true. No values overlap, meaning that the table does represent y as a function of x.

For Part B, we simply just substitute "4" in for "x" and solve from there.

\[y=2(4)+12\]
\[y=8+12\]
\[y=20\]

This means that total cost for renting a bowling alley is 20 dollars.