Chapter 3.2, Problem 1AYU

Plot the points $\left(1,5\right),\left(2,6\right),\left(3,9\right),\left(1,12\right)$ in the Cartesian plane. Is the relation $\left\{\left(1,5\right),\left(2,6\right),\left(3,9\right),\left(1,12\right)\right\}$ a function? Why? (pp. 2 and 57-60)

To determine

To graph: The given points in the Cartesian plane and determine whether the set of all the given points is a function.

Answer to Problem 1AYU

Solution:

Explanation of Solution

Given:

The given points are $(1,5), (2,6), (3,9), (1,12)$.

Graph:

Interpretation:

We can plot the given set of points by considering the points using the general format $(x,y)$ and then plot the points according to both the coordinates of $x$ and $y$.

The given set $\{(1, 5), (2, 6), (3, 9), (1, 12)\}$ is a function because we can see that for each value of the $x$-coordinate there is exactly one $y$ value.

Thus, it satisfies the definition of a function.

Therefore, the given set is a function.