Q.3 - Precalculus Enhanced with Graphing Utilities

Question

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

True or False For a function $y=f\left(x\right)$, for each $x$ in the domain, there is exactly one element$y$ in the range.

Step-by-Step Solution

Answer

The statement for a function $y=f\left(x\right)$, for each $x$ in the domain, there is exactly one element $y$ in the range is a true statement.

Given information

Consider the statement that for a function  $y=f\left(x\right)$, for each$x$ in the domain, there is exactly one element $y$ in the range.

The main objective is to determine whether the given statement is true or false.

Explanation

The definition of a function $y=f\left(x\right)$ is defined as the relation from $X$ into $Y$ such that each element of $X$ associated with exactly one element of $Y$.

Then by the definition of the function, the given statement is true.