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No, the graph does not represent a function because it does not pass the vertical line test.
<h2>What is a function?</h2>A function is when each x-value only has one y-value. We know that a graph represents a function if it passes the vertical line test.
<h3>Vertical Line Test</h3>To pass the test, any vertical line that we draw on the graph should only touch one point.
A vertical line is a straight line that goes from top to bottom.
- Draw vertical lines through points on the graph, like in the photo below.
- Check if any vertical lines touch more than one point.
The yellow vertical line touches two points, which is more than one. So, the graph does not pass the test. This graph is does not represent a function.
The most direct form to graph a line, is to find two points of it and connect them with a line.
Here we have:
Let's find the point where x = 0. To do this, we replace the x in the equation by 0:
We have our first point: (0, -6)
Next let's find the point where y = 0. Again, we replace y in by 0 in the equation:
We have our second point, (3, 0)
Now all we have to do is plot the points (0, -6) and (3, 0) in the plane, and connect them with a line, and then the line is graphed
The line should look like this:
