Sure! Let's graph the function [tex]\( y = 4 \cdot 5 \)[/tex].
1. Understanding the function:
First, we need to understand the mathematical form of the function. The function given is [tex]\( y = 4(5) \)[/tex]. Simplifying this, we get:
[tex]\[
y = 4 \cdot 5 = 20
\][/tex]
This simplifies to:
[tex]\[
y = 20
\][/tex]
2. Type of function:
The equation [tex]\( y = 20 \)[/tex] represents a constant function. This means that, regardless of the value of [tex]\( x \)[/tex], [tex]\( y \)[/tex] will always be 20.
3. Drawing the graph:
To graph this function, follow these steps:
- Draw the Cartesian plane with the x-axis and y-axis.
- Since [tex]\( y = 20 \)[/tex] for all values of [tex]\( x \)[/tex], you need to draw a horizontal line that passes through [tex]\( y = 20 \)[/tex].
4. Plotting points:
To ensure accuracy, let's plot a few points:
[tex]\[
\begin{array}{c|c}
x & y \\
\hline
-10 & 20 \\
-5 & 20 \\
0 & 20 \\
5 & 20 \\
10 & 20 \\
\end{array}
\][/tex]
5. Drawing the line:
- Plot the points [tex]\((-10, 20)\)[/tex], [tex]\((-5, 20)\)[/tex], [tex]\((0, 20)\)[/tex], [tex]\((5, 20)\)[/tex], and [tex]\((10, 20)\)[/tex] on the Cartesian plane.
- Draw a horizontal line through all of these points.
So, the graph of the function [tex]\( y = 20 \)[/tex] is a straight horizontal line passing through the [tex]\( y \)[/tex]-axis at [tex]\( y = 20 \)[/tex].
Graphical Representation:
```
y
^
|
30|-----------------------
25|-----------------------
20|----●----●----●----●----●
15|-----------------------
10|-----------------------
5|-----------------------
0|----------|-----------|----> x
-10 0 10
```
All points where [tex]\( x \)[/tex] takes any value are aligned along the line where [tex]\( y = 20 \)[/tex]. This represents the constant function graph.
