The graph in the image shows a horizontal line at $y = 2$. This indicates that the function is a constant linear function, meaning that for all values of $x$, the output (or $y$-value) is always $2$.

Domain:

The domain of a function is the set of all possible input values (in this case, $x$-values). Since this is a linear function that extends infinitely in both directions along the $x$-axis, the domain includes all real numbers.

• Domain: $(-\infty, \infty)$ or "all real numbers."

Range:

The range of a function is the set of all possible output values (in this case, $y$-values). For this graph, the $y$-value is always $2$ no matter the $x$-value, so the range consists of just the single value $2$.

• Range: $\{ 2 \}$.

Would you like more details on how the domain and range are determined?

Here are 5 related questions you might find useful:

1. What is the general form of a constant function?
2. How do you find the slope of a horizontal line?
3. Can a linear function ever have a limited domain or range?
4. What is the difference between a horizontal and vertical line on a graph?
5. How would the domain and range change if the graph were a vertical line instead?

Tip: In a linear equation $y = mx + b$, if $m = 0$, the function is constant, and the graph is a horizontal line.