Q62. - 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.

$y=-x+4$

Step-by-Step Solution

Answer

The given function is continuous 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 equation of a function is $y=-x+4$.

Step 3 – Check whether the function is discrete or continuous.

The given function is a linear function because it is in the form of $y=mx+b$, where $m=-1$ is the slope and $b=4$ is the $y-$intercept. 

The graph of a linear function is always a straight line. It means the graph of the given equation is a single non disconnected line.

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

 

Thus, the given function is a continuous function.