#### To determine

**To find:**

(a) Define a one to one function.

(b) Identify how to if a graph is a one to one function.

#### Answer

(a) Definition given below

(b) Definition of one to one function given below.

#### Explanation

(a) **Definition**: A function *f* is said to be one to one if it never takes the same value twice, i.e., for any two distinct points in the domain, their images are also distinct.

Symbolically, *X*_{1} ≠ X_{2} ⇒ f(X_{1} ) ≠ f(X_{2}).

**Example**: Let *f* be a mapping from domain *A* to co-domain *B*, i.e., *f:A→B*, defined as *f(x) = x*. Then for any two distinct points *x*_{1}_{} and *x*_{2}_{} in *A*, *f(x*_{1}) = x_{1}_{} and *f(x*_{2}) = x_{2}_{,} i.e., *f(x*_{1}) ≠ f(x_{2}).

Thus, the function *f* is one to one.

(b) If you want to see whether or not the given function is one to one, you can use the HORIZONTAL LINE TEST by just looking at the graph. This condition is described as follows:

A function is one to one if and only if no horizontal line intersects its graph more than once.

**Conclusion:**

(a) See the Definition

(b) See the Definition of one to one function.