Given the function below, fill in the table of values and use the table values to graph.
[tex]y=-2[/tex]
\begin{tabular}{|c|c|}
\hline [tex]x[/tex] & [tex]y=-2[/tex] \\
\hline-3 & \\
\hline-2 & \\
\hline-1 & \\
\hline 0 & \\
\hline 1 & \\
\hline 2 & \\
\hline 3 & \\
\hline
\end{tabular}
Answer (2)
The function y = − 2 is a constant function.
The value of y is always − 2 regardless of the value of x .
The graph is a horizontal line passing through y = − 2 .
The table is filled with y = − 2 for all x values, and the final answer is a horizontal line at y = − 2 .
Explanation
Understanding the Problem The problem asks us to complete a table of values for the function y = − 2 and then graph the function using these values.
Completing the Table The function y = − 2 is a constant function, meaning that the value of y is always − 2 regardless of the value of x . Therefore, we can fill in the table with y = − 2 for all given x values.
Filled Table Here's the completed table:
x
y = -2
-3
-2
-2
-2
-1
-2
0
-2
1
-2
2
-2
3
-2
Plotting the Points Now, we plot these points on a coordinate plane. The points are ( − 3 , − 2 ) , ( − 2 , − 2 ) , ( − 1 , − 2 ) , ( 0 , − 2 ) , ( 1 , − 2 ) , ( 2 , − 2 ) , and ( 3 , − 2 ) .
Graphing the Function Since all the y -values are the same, the graph will be a horizontal line passing through y = − 2 .
Final Answer The graph of the function y = − 2 is a horizontal line at y = − 2 .
Examples
Imagine you're tracking the temperature inside a freezer, and it consistently stays at -2 degrees Celsius. This constant temperature can be represented by the function y = − 2 , where y is the temperature and x is the time. No matter how much time passes (different values of x ), the temperature remains the same. This concept is useful in many real-world situations where a value remains constant regardless of other variables.
The function y = − 2 is a constant function, meaning it always equals − 2 regardless of x . The completed table indicates that for each value of x , the corresponding value of y is − 2 . The graph is a horizontal line at y = − 2 .
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