Horizontal Line Test Examples Math

Once we have determined that a graph defines a function an easy way to determine if it is a one to one function is to use the horizontal line test.

Horizontal line test examples math. Draw horizontal lines through the graph. Determine the horizontal line equation whose y intercept is 0 2 solution. The graph of the function is a parabola which is one to one on each side of x 2 thus passing the horizontal line test with the restricted domain x 2. It fails the vertical line test and so is not a function.

It is defined as the part of the horizontal line that is limited by the two points. For example on the interval π 2 π 2 y sin x is one to one and therefore has an inverse for that interval. When a and b are subsets of the real numbers we can graph the relationship. A function f is invertible if and only if no horizontal straight line intersects its graph more than once.

So let us see a few examples to understand what is going on. The horizontal line test is a convenient method that can determine whether a given function has an inverse but more importantly to find out if the inverse is also a function. A test use to determine if a function is one to one if a horizontal line intersects a function s graph more than once then the function is not one to one. If any horizontal line intersects the graph more than once then the graph does not represent a one to one function.

However if you take a small section the function does have an inverse. Equation of horizontal line always takes the form of y k where k is the y intercept of the line for instance in the graph below the horizontal line has the equation y 1 as you can see in the picture below the line goes perfectly sideways at y 1. This is not a function because we have an a with many b it is like saying f x 2 or 4. The function y f x is a function if it passes the vertical line test it is a one to one function if it passes both the vertical line test and the horizontal line test.

Remember that it is very possible that a function may have an inverse but at the same time the inverse is not a function because it doesn t pass the vertical line test. Y intercept 0 2 we know that the general equation of the horizontal line is y k. For example at first glance sin x should not have an inverse because it doesn t pass the horizontal line test. Properties of horizontal lines.

The horizontal line test is an important tool to use when graphing algebraic functions. Let us have a on the x axis and b on y and look at our first example. On a graph. Those two points are called the endpoints.

To find the inverse of a function such as this one an effective method is to make use of the quadratic formula.