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?

1 Answer
May 3, 2018

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.