Question

How do you use the horizontal line test to determine whether the function `f(x)=1/8(x+2)^2-1` is one to one?

Answer 1

The horizontal line test is to drawing several horizontal lines, `y=n,ninRR`, and see if any lines cross the function more than once.

A one-to-one function is a function where each `y` value is given by only one `x` value,, whereas a many-to-one function is a function where multiple `x` values can give 1 `y` value.

If a horizontal line crosses the function more than once, then it means that the function has more than one `x` value which gives one value for `y`.

In this case, doing so will give two intersections for `y>1`

Example:
graph{(y-(x+2)^2/8+1)(y-1)=0 [-10, 10, -5, 5]}

The line `y=1` crosses `f(x)` twice and is not a one-to-one function.