Function Checks

==2024-11-14

Vertical And Horizontal Checks

Vertical Line Check

Theory

To check if a curve is a function or not, you do a vertical check.

If a vertical line can intersect the graph at two points then it's

not a function. Why? Because if so, one input will give two output and That is not the defination of Function

$y = sin x$ is a function
\sin x
x=4

$x^{2} + y^{2} = 1$ is not a function
x^2+y^2=16
x=3

Horizontal Line Check

Theory

To find if a function is one to one or not, use horizontal line check.

Why?

Because in graph, for different x, the y is same.

$y = x^{2}$ is a function but not one to one.
y=x^2
x=1

PTR

function → |
one to one → -