Q61. - Algebra 2

Question

A function whose graph consists of disconnected points is called a discrete function. A function whose graph you can draw without lifting your pencil is called a continuous function. Determine whether each function is discrete or continuous.

$\left\{\left(-3,0\right),\left(-1,1\right),\left(1,3\right)\right\}$

Step-by-Step Solution

Answer

The given function is discrete function.

Step 1 – Definition of discrete and continuous function.

A function is called discrete if its graph consists of disconnected points.

A function is called continuous if its graph has a single line or curve.

Step 2 – Given information.

The given function is $\left\{\left(-3,0\right),\left(-1,1\right),\left(1,3\right)\right\}$.

Step 3 – Draw the graph of the given function.

Plot the points $\left(-3,0\right),\left(-1,1\right),\left(1,3\right)$ on a coordinate plane as shown below:

Step 4 – Check whether the function is discrete or continuous.

From the above graph it is clear that the graph consists of disconnected points.

Using the definition of discrete function, it is clear that the given function represents a discrete function.

Thus, the given function is a discrete function.