Chapter 2.2, Problem 38AYU

To determine

Whether a graph that consists of a single point the graph of a function and to write the equation of such a function.

Answer to Problem 38AYU

The graph of this function is the single point $\left(1,1\right)$ and its equation is $1=1$ .

Explanation of Solution

Let $X=\left\{1\right\}$ and $Y=\left\{1\right\}$ be two nonempty sets. A function from $X$ into $Y$ is a relation that associates with each element of $X$ exactly one element of $Y$ .

So, the relation $\left(1,1\right)$ is a function from $X$ to $Y$ . The graph of this function is the single point $\left(1,1\right)$ and its equation is $1=1$ .