Answer
398.1k+ views
Hint: Consider \[y=\sqrt{x}\] as the parent root function. Now, consider some values of x which are perfect squares like 1, 4, 9 and find the value of y for these points. Find the corresponding values of y for the function \[y=3\sqrt{x}\]. Plot the obtained points and draw the graph of the two functions on the same graph paper to compare them.
Complete step by step answer:
Here, we have been provided with the function \[y=3\sqrt{x}\] and we are asked to draw its graph and compare it with the graph of parent square root function. But first let us know what is meant by the term ‘parent square root function’.
Now, as we can see that the function \[y=3\sqrt{x}\] contains 3 as the coefficient of \[\sqrt{x}\], so in the parent square root function the coefficient of \[\sqrt{x}\] will be 1. So, the function would be \[y=\sqrt{x}\]. To draw the graph we will need some parts, so assuming some values of x which are perfect square, we can draw the following table: -
So, drawing the graph of the two functions according to the points obtained, we get,
From the above graph we can see that the curve \[3\sqrt{x}\] will always be three times the curve \[\sqrt{x}\] at any particular point x. That means we can say that \[3\sqrt{x}\] is stretched three times \[\sqrt{x}\]. The curve \[3\sqrt{x}\] always lies above the curve \[\sqrt{x}\].
Note: One may note that the two curves are half part of the parabola having the general equation \[{{y}^{2}}=kx\]. We have taken only half part because here y will not be negative as we have considered only positive square root and the value of ‘k’ is also positive for both the curves. Remember that you cannot choose negative values of x because if you will do so then the value of \[\sqrt{x}\] will become imaginary and we do not sketch imaginary values on the cartesian plane. There is another type of plane known as ‘argand plane’ for plotting complex numbers.
Complete step by step answer:
Here, we have been provided with the function \[y=3\sqrt{x}\] and we are asked to draw its graph and compare it with the graph of parent square root function. But first let us know what is meant by the term ‘parent square root function’.
Now, as we can see that the function \[y=3\sqrt{x}\] contains 3 as the coefficient of \[\sqrt{x}\], so in the parent square root function the coefficient of \[\sqrt{x}\] will be 1. So, the function would be \[y=\sqrt{x}\]. To draw the graph we will need some parts, so assuming some values of x which are perfect square, we can draw the following table: -
x | 1 | 4 | 9 | 16 |
\[\sqrt{x}\] | 1 | 2 | 3 | 4 |
\[3\sqrt{x}\] | 3 | 6 | 9 | 12 |
So, drawing the graph of the two functions according to the points obtained, we get,
![seo images](https://www.vedantu.com/question-sets/35fe66fb-4012-42ac-80ea-5a931b6392648922667589488015101.png)
From the above graph we can see that the curve \[3\sqrt{x}\] will always be three times the curve \[\sqrt{x}\] at any particular point x. That means we can say that \[3\sqrt{x}\] is stretched three times \[\sqrt{x}\]. The curve \[3\sqrt{x}\] always lies above the curve \[\sqrt{x}\].
Note: One may note that the two curves are half part of the parabola having the general equation \[{{y}^{2}}=kx\]. We have taken only half part because here y will not be negative as we have considered only positive square root and the value of ‘k’ is also positive for both the curves. Remember that you cannot choose negative values of x because if you will do so then the value of \[\sqrt{x}\] will become imaginary and we do not sketch imaginary values on the cartesian plane. There is another type of plane known as ‘argand plane’ for plotting complex numbers.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)