Question

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

Answer 1

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:

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

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

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.