How do you use the horizontal line test to determine whether the function #g(x)=(4-x)/6# is one to one?

1 Answer
Jun 17, 2018

see below

Explanation:

a function that passes the horizontal line test intersects any given horizontal line at only one point.
a function that fails the horizontal line test will intersect some horizontal lines at more than one point.

all horizontal lines have #y# as a constant, and so the equation of their lines can be something like #y = 1, y = 11#, etc.

here are some horizontal lines that help determine if ##g(x) = (4-x)/6# is a one-to-one function:

the function #g(x) = (4-x)/6# intersects with the line #y = 10# at #(-56, 10)# as shown:

desmos.com/calculator

intersects with the line #y = 2# at #(-56, 10)# as shown:

desmos.com/calculator

and intersects with the line #y = -6# at #(40, -6)# as shown:

desmos.com/calculator

in reality, you would only need one line to test this function; the three examples are simply there to show that you can use a horizontal test for any constant value of #y#, and the function will cut each horizontal line only once.