Home
Class 12
MATHS
Given the graph of the function y=f(x),...

Given the graph of the function `y=f(x)`, draw the graph of `y ="sgn"f(x)`.

Text Solution

Verified by Experts

From the graph, `f(x) gt 0` for ` x lt -3 or x gt 1 `
`therefore " ""sgn"(f(x))= 1` for `x in (-oo, -3) uu ( 1, oo)`
`" "f(x) lt 0` for `x in (-3, 1)`
`therefore" ""sgn"(f(x)) = -1 ` for `x in (-3, 1)`
`" "f(x) =0` for `x= -3, 1`
`therefore " " "sgn (f(x))= 0` for `x = -3, 1`
Hence the graph of `y="sgn"(f(x))` 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 y=x-sinx

Draw the graph of y = sin 2^(x).

Draw the graph of the function f(x)=x^2

Draw the graph of y=x//"ln "x

Draw the graph of y= x-sinx

Draw the graph of y = x sin x.

Draw the graph of the function f(x) =x^x .

Draw the graph of y=|x| .

Draw the graph of y=|x|+2

CENGAGE-GRAPHS OF ELEMENTARY FUNCTIONS -Exercise
  1. Given the graph of the function y=f(x), draw the graph of y ="sgn"f(x...

    Text Solution

    |

  2. Draw the graph of y= (1)/((1//x)).

    Text Solution

    |

  3. (a) Draw the graph of f(x) = ={{:(1",",, |x| ge 1), ((1)/(n^(2)) ",",,...

    Text Solution

    |

  4. Sketch the regions which points satisfy |x+y| ge 2.

    Text Solution

    |

  5. Sketch the region satisfying |x| lt |y|.

    Text Solution

    |

  6. Let f:R→R:f(x)=(x+1) and g:R→R:g(x)=(x^2−2). Write down the formulae f...

    Text Solution

    |

  7. Draw the graph of y= (x-1)/(x-2).

    Text Solution

    |

  8. The following figure shows the graph of f(x) =ax^(2)+bx +c, then find ...

    Text Solution

    |

  9. The entire graph of the equation y=x^2+k x-x+9 in strictly above the x...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |