Exercise 1 Page 159

For a relation to be a function, each $x\text{-}$value can only be paired with one $y\text{-}$value, but one $y\text{-}$value can be paired with multiple $x\text{-}$values.

Is the Relation a Function?

Let's look at the given values.

Since each input $x$ has only one output, the relation in the table is a function.

Is the Relation Linear?

To determine whether this function is linear or nonlinear, we observe the changes in $x$ and $y.$ If both of these rates of change are constant, we can conclude that the function is linear.

We can see that as $x$ increases by $1,$ $y$ increases by different amounts. The rate of change is not constant. Therefore, the function is nonlinear.