Is the given graph a function?
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Is the given graph a function?
It is important to remember that a function is an equation that assigns to each element in domain X one and only one element in range Y
Let's note that in the graph:
In other words, there are two values for the same number.
Therefore, the graph is not a function.
No
Determine whether the following table represents a constant function:
The vertical line test is a visual way to check if a graph represents a function. Draw or imagine any vertical line through the graph. If it touches the graph at more than one point, it's not a function.
An ellipse is symmetric around both axes, so most vertical lines through it will intersect two points. For example, at x = 0, we get both y = 2 and y = -2, violating the function rule.
Correct! Circles fail the vertical line test just like ellipses. Any vertical line through a circle (except at the very edges) intersects the circle at two points.
Yes! If you take just the top half or bottom half of an ellipse, it would pass the vertical line test and represent a function.
A vertical parabola (like ) passes the vertical line test because each x-value gives only one y-value. But a horizontal parabola would fail, just like this ellipse!
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