Which of the following graphs represents a function?

1st Graph

Step-by-step explanation:

A simple way to test if a relation may be taken as a function is by applying the Vertical Line Test. If a Vertical Line crosses the graph only once, then it is a function. In this question, only the first one can be considered to be a function.

Because in other words, only the first graph shows one value for x corresponding to another for y value. Not the case for the second and the third graph displaying two values for x for each y value.

Graph (a) is function as it passes the vertical line test as well as the horizontal line test.

Further explanation:

Explanation:

The output values of the function are known as range and the input values on which function is defined is known as the domain of the function.

The one-to-one function is a function in which every value of the range has exactly one pre-image in the domain.

One-to-one function always passes the vertical line test and the horizontal line test.

Graph (a) is function as it passes the vertical line test as well as the horizontal line test.

Graph (b) is not a function as it doesn’t passes the vertical line test as well as the horizontal line test.

Graph (c) is not a function as it doesn’t passes the vertical line test as well as the horizontal line test.

Graph (d) is not a function as it doesn’t passes the vertical line test as well as the horizontal line test.

Learn more:

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Relation and Function

Keywords: relations, functions, all relation are functions, all functions are relations, no relations are functions, no functions are relation, one-to-one, onto, graph representation, paired, y-value, x-values, origin.

step-by-step explanation: