Answer
a.
The Vertical Line Test
consists of checking whether any vertical line intersects a graph in more than one point,
in which case we say the graph has failed the test.
If it passes the test, then the graph represents a function.
b.
The Horizontal Line Test
consists of checking whether any horizontal line intersects a graph of a function in more than one point.
If it does, we say the graph fails the test.
If there are no such horizontal lines, the graph passes the test and the function is one-to-one.
Work Step by Step
A graph consists of points (x, f(x)).
f(x) defines a relation, that can be a function, or it may not be one.
a.
The Vertical Line Test
consists of checking whether any vertical line intersects a graph in more than one point,
in which case we say the graph has failed the test.
If it passes the test (no such vertical lines exist), then the graph represents a function.
The reason behind this is that
a function can have only one y-value assigned to a particular x.
Failing the vertical line test means that there are x's that have more than one y assigned.
b.
The Horizontal Line Test
consists of checking whether any horizontal line intersects a graph of a function in more than one point.
If it does, we say the graph fails the test.
If there are no such horizontal lines, the graph passes the test and the function is one-to-one.
One-to-one functions are such that no y-coordinate can be assigned to two different x-values.