Table of Contents
How do you tell if a graph represents a function?
Inspect the graph to see if any vertical line drawn would intersect the curve more than once. If there is any such line, the graph does not represent a function. If no vertical line can intersect the curve more than once, the graph does represent a function.
Which graph passes the vertical line test?
The graph of a function always passes the vertical line test. The test stipulates that any vertical line drawn through the graph of the function passes through that function no more than once. This is a visual illustration that only one y value (output) exists for every x value (input), a rule of functions.
How can you use the vertical line test and the horizontal line test to determine whether a graph represents a function and whether the graph is invertible?
A function f(x) has an inverse, or is one-to-one, if and only if the graph y = f(x) passes the horizontal line test. A graph represents a one-to-one function if and only if it passes both the vertical and the horizontal line tests.
How do you tell if something is a function without graphing?
If a vertical line crosses the relation on the graph only once in all locations, the relation is a function. However, if a vertical line crosses the relation more than once, the relation is not a function. Using the vertical line test, all lines except for vertical lines are functions.
Is a circle on a graph a function?
A circle can be described by a relation (which is what we just did: x2+y2=1 is an equation which describes a relation which in turn describes a circle), but this relation is not a function, because the y value is not completely determined by the x value.
What is vertical line test used for?
The vertical line test can be used to determine whether a graph represents a function. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because a function has only one output value for each input value.
Can a function fail the vertical line test?
Since a function can only have one unique output value for y for any input value of x, the function fails the Vertical Line Test and is therefore not a function.
Is the vertical line test to determine which graph does not represent a function?
Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
What is the vertical line test in functions?
The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines. and, as a result, any vertical line in the plane can intersect the graph of a function at most once.
What is an example of a vertical line?
It is a straight line which goes from top to bottom and bottom to top. Any point in this line will have the same value for the x-coordinate. For example, (2,0), (3,0) (-4,0), etc. are the points of vertical lines.
Can a vertical line be a function?