If the domain and range of a function consists of real numbers, then you can graph it by plotting all ordered pairs (x, f(x)). Remember "y" = f(x). How can you tell by looking at a graph if it represents a function?
It is easier to tell which graph not a function.
If there exists any vertical line x=k that intersects the graph at more than one point, the graph is not a function. This is call the vertical line test.
To determine if a graph represents a function, you can apply the vertical line test. Here's how:
1. Look at the graph and observe the plotted points or the curve.
2. Imagine drawing vertical lines at different x-values across the entire graph.
3. If any vertical line intersects the graph in more than one point, then it does not represent a function.
4. If each vertical line intersects the graph at most once, then it does represent a function.
The reason behind this test is that for a graph to represent a function, every element in the domain must have a unique corresponding element in the range. By using vertical lines, you are essentially checking if the function passes the "one-to-one" test.
Remember, for a graph to represent a function, it must pass the vertical line test.