Characteristic of One-to-one Functions

[nycmathguy]

Ron Larson stated:

"If no horizontal line intersects the graph of f at more than one point, then no y-value corresponds to more than one x-value. This is the essential characteristic of one-to-one functions."

Can you provide two sample graphs to make clear the above statement?

 

[MathLover1]

If no horizontal line intersects the graph of the function f in more than one point, then the function is 1 -to- 1 .
example:
y=x^3
horizontal line y=2

2.
y=sqrt(x)+1
y=2

 

[nycmathguy]

If no horizontal line intersects the graph of the function f in more than one point, then the function is 1 -to- 1 .
example:
y=x^3
horizontal line y=2

View attachment 249

2.
y=sqrt(x)+1
y=2

Ok. This is fairly easy.