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Good morning!

How to draw the graph of the following function and discuss the increasing and decreasing intervals of y.

$y = $x$ + \sqrt[]{x^2}$

Also, I would like to know free online graphing calculator

Thanks in advance.

kalanidi
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2 Answers2

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Hint: Recall that $\sqrt{x^2} = |x|$, so

$$f(x) = x + |x| = \left\{\begin{array}{lr} 2x &: \text{ if } x \ge 0 \\ 0 &: \text{ if } x < 0 \end{array}\right.$$

For an online graphic calculator, I would suggest Wolfram Alpha.

  • ! Thank you for your post. If we have three funtions like y = -2 at x>0, y = 0.5 at x = 0 and y = - x^3 at x < 0. How to draw the graph of these functions in a single graph. Kindly answer, as I am unable to draw this three functions at Wolfram Aplpha. But your solution for my first questions is very good. Thanks again. – kalanidi Oct 19 '13 at 04:48
  • @kalanidi Here is a link to documentation. Then entry syntax for your question is > Plot[Piecewise[{{-x^3, x < 0}, {0.5, x = 0}, {2, x > 0}}], {x, -3, 3}] –  Oct 19 '13 at 04:51
  • ! Thank you so much. Still, I am unable to find. Can you send the lick of Wolfram Alpha of my graph please.. – kalanidi Oct 19 '13 at 04:55
  • @kalanidi Just go to WolframAlpha and enter the command from Plot to the last ] verbatim. –  Oct 19 '13 at 04:57
  • ! I did. But, I dint get any graph. So can you do for me? and then just paste the web lick here. – kalanidi Oct 19 '13 at 04:58
  • @kalanidi http://www.wolframalpha.com/input/?i=Plot%5BPiecewise%5B%7B%7B-x%5E3%2C+x+%3C+0%7D%2C+%7B0.5%2C+x+%3D+0%7D%2C+%7B2%2C+x+%3E+0%7D%7D%5D%2C+%7Bx%2C+-3%2C+3%7D%5D –  Oct 19 '13 at 04:59
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You can try Calcpad, it is free for both online and desktop:

http://calcpad.net/Calculator

Just type the following:

f(x) = x + sqr(x^2)

$Plot{f(x) @ x = -1 : 1}

This is the graph you will get

Plot 1

You can also define a function with three segments as follows:

f(x) = -2*(x > 0) + 0.5*(x ≡ 0) - x^3 * (x < 0)

The conditions in the brackets return 1 for "true" and 0 for "false" which makes possible to create an expression like the above one. It will evaluate correctly:

f(-2) = 8

f(0) = 0.5

f(2) = -2

However, it will not plot correctly as one function. You have to use the "multiple" plot command. It has the following syntax:

$Plot{x1 | y1 & x2 | y2 & x3 | y3 @ x = a : b}

For your example, type the following...

$Plot{x*(x > 0) | -2 & 0 | 0.5 & x*(x < 0) | -x^3*(x < 0) @ x = -1 : 1}

...and you will get this plot:

Plot 2

Ned
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