Home
Class 12
MATHS
Draw the graph of f(x) = x|x|....

Draw the graph of `f(x) = x|x|`.

Text Solution

Verified by Experts

`y =f (x) = x|x|= {{:(x*x= x^(2)",",, x ge 0 ), (x*(-x)= -x^(2)",",, x lt 0):}`
Thus, for `x ge 0`, we have, parabola `y=x ^(2)`, which is concave upward, and for `x lt 0`, we have the parabola `y= -x^(2)`, which is concave downward.
Hence the graph of the function is as shown in the following figure.
Promotional Banner

Topper's Solved these Questions

  • GRAPHS OF ELEMENTARY FUNCTIONS

    CENGAGE|Exercise Exercise|34 Videos

  • GRAPHS OF POLYNOMIAL AND RATIONAL FUNCTIONS

    CENGAGE|Exercise Exercises|4 Videos

  • GRAPHS OF TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise|22 Videos

Similar Questions

Explore conceptually related problems

Draw the graph of f(x) = |tan x| + |cot x|.

Draw the graph of f(x) = 2x+3x^(2//3) and discuss the type of non-differentiability for the function. Also find the point of inflection.

Draw the graph of f(x) = sec x + "cosec " x, x in (0, 2pi) - {pi//2, pi, 3pi//2} Also find the values of 'a' for which the equation sec x + "cosec " x = a has two distinct root and four distinct roots.

Draw the graph of f(x) = xcosx-sinx, x in [-3pi, 3pi]

Draw the graph of y=|x| .

Draw the graph of f(x)=(x-1) |(x-2)(x-3)|. .

Draw the graph of f(x) = "sgn"(x^(3) -x) .

Draw the graph of f(x) = {{:(x^(3)","x^(2) lt 1), (x","x^(2)le1):}

Draw the graph of f(x) = [x^(2)], x in [0, 2) , where [*] denotes the greatest integer function.

Draw the graph of f(x) = e^(x)/(1+e^(x)) . Also find the point of inflection.

CENGAGE-GRAPHS OF ELEMENTARY FUNCTIONS -Exercise
  1. The entire graph of the equation y=x^2+k x-x+9 in strictly above the x...

    Text Solution

    |

  2. If x^2+2a x+a<0AAx in [1,3], the find the values of adot

    Text Solution

    |

  3. Draw the graph of f(x) = x|x|.

    Text Solution

    |

  4. Draw the graph of the function: Solve |(x^2)/(x-1)|lt=1 using the grap...

    Text Solution

    |

  5. Draw the graph of y = |x^(2) - 2x|-x.

    Text Solution

    |

  6. Draw the graph of y =2^(x)"," x^(2)-2x le 0

    Text Solution

    |

  7. Find the roots of the equation by factorization: 2x^2-x-1

    Text Solution

    |

  8. Divide 16(x^2yz + xy^2z+xyz^2) by 4xyz

    Text Solution

    |

  9. Find the set of real value(s) of a for which the equation |2x+3|+2x-3|...

    Text Solution

    |

  10. Draw the graph of y=|x|.

    Text Solution

    |

  11. Draw the graph of y=1/(log(e)x)

    Text Solution

    |

  12. Find the number of real solutions to the equation log(0.5)x=|x|.

    Text Solution

    |

  13. Draw the graph of f(x)= x+ [x], where [*] denotes the greatest integer...

    Text Solution

    |

  14. Given f(x) is a periodic function with period 2 and it is defined as ...

    Text Solution

    |

  15. Sketch the region of relation [x] + [y] = 5, x, y ge 0, where [*] deno...

    Text Solution

    |

  16. Draw the graph of y= 2^({x}), where {*} represents the fractional par...

    Text Solution

    |

  17. Let f(x) = ([x]+1)/({x}+1) for f: [0, (5)/(2) ) to ((1)/(2) , 3], whe...

    Text Solution

    |

  18. Draw the graph of y= 2^({x}), where {*} represents the fractional par...

    Text Solution

    |

  19. Find tha area of the region containing the points (x, y) satisfying 4...

    Text Solution

    |

  20. Draw the graph of y= sqrt (x^(2)-1)

    Text Solution

    |