Answer

Verified

427.2k+ views

**Hint:**A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output. It is denoted as $f:{\text{X}} \to {\text{Y}}$, a function from X to Y.

It means that if the object x is in the set of inputs (called the domain) then the function f will relate to exactly one object f(x).

**Complete step-by-step answer:**

A relation between two sets is a collection of ordered pairs containing one object from each set.

A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.

Given, $x \in R,y \in R$ and a relation in between x and y as: \[{y^2} = 4ax \Rightarrow y = 2\sqrt {ax} .......\left( i \right)\]

Equation (i) represents for every value of x, there exists one value of y.

Thus, by definition of function, each set of values of inputs has a set of possible outputs, i.e., If $x = 0$ , then $y = 2\sqrt {a.0} = 0$

If $x = 1$, then $y = 2\sqrt {a.1} = 2\sqrt a $

If $x = a$, then $y = 2\sqrt {a.a} = 2a$…… etc.

Hence, ${y^2} = 4ax$ is a function of x.

**Note:**To determine whether a relation is a function, by using the vertical line test on the graph of a relation (in between two variables).If a vertical line crosses the relation on the graph only once in all locations, the relation is a function. And if a vertical line crosses the relation more than once, the relation is not a function.

Also, please note that a given function is an equation of parabola whose focus is (0, 0) and the graph of it is symmetrical about the x – axis so it is called the axis of symmetry for such equations of parabola. Graphs of parabolas are always U-shaped curves, which may be symmetrical about X- axis or negative X – axis or Y – axis or negative Y – axis.

Recently Updated Pages

Which of the following is correct regarding the Indian class 10 social science CBSE

Who was the first sultan of delhi to issue regular class 10 social science CBSE

The Nagarjuna Sagar project was constructed on the class 10 social science CBSE

Which one of the following countries is the largest class 10 social science CBSE

What is Biosphere class 10 social science CBSE

Read the following statement and choose the best possible class 10 social science CBSE

Trending doubts

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Difference Between Plant Cell and Animal Cell

Why is the Earth called a unique planet class 6 social science CBSE