Exercise 6 Page 159

The $x\text{-}$ and $y\text{-}$intercepts occur when the function crosses the $x\text{-}$ and $y\text{-}$axes, respectively. At the $x\text{-}$intercept, $y$ is $0.$ Similarly, at the $y\text{-}$intercept, $x$ is $0.$ We can identify these coordinate pairs in the given table,

We can see that when $x=0,$ $y=\text{-}24.$ This means that our $y\text{-}$intercept is $\text{-}24.$ We can also see that when $y=0,$ $x=12,$ meaning that our $x\text{-}$intercept is $12.$

Interpreting the Intercepts

The table involves a diver's depth as a function of time. The $y\text{-}$intercept tells us that when their position is first measured at $0$ seconds, the diver is at a depth of $24$ meters. The $x\text{-}$intercept tells us how long it took the diver to surface. We know that after $12$ seconds have passed, the diver's depth is $0$ meters, which suggests that it took them $12$ seconds to surface.

By the way, if you are ever scuba diving, DO NOT surface this fast or you can badly hurt yourself!