Home
Class 12
MATHS
Draw the graph of y= |x-1|+3|x-2|-5|x-4|...

Draw the graph of `y= |x-1|+3|x-2|-5|x-4|` and find the values of `lamda` for which the equation `f(x) = lamda` has roots of opposite sign.

Text Solution

Verified by Experts

We have `y=f(x) = |x-1|+ 3|x-2|- 5|x-4|`
`" "={{:(1-x+6-3x-20+5x",",, xlt1), (x-1+6-3x-20+5x",",,1le x le 2), (x-1+3x-6-20+5x",",,2 lt x lt 4),(x-1+3x-6+20-5x",",,xge 4):}`
`" "={{:(-13+x",",, xlt1), (-15+3x",",,1le x le 2), (-27+9x",",,2 lt x lt 4),(13-x",",,xge 4):}`
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 Exercise|13 Videos

  • GRAPHS OF TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise|22 Videos

Similar Questions

Explore conceptually related problems

find the set of values of a for which roots of the equation x^(2)+2(a-1)x+(a+5) are of opposite sign

The value of m for which the equation x^(3)-mx^(2)+3x-2=0 has two roots equal rea magnitude but opposite in sign,is

Find the value of lamda and mu for which the system of equations x+y+z=6 3x+5y+5z=26 x+2y+lamdaz=mu has no solution

The values of lamda for which the line y=x+ lamda touches the ellipse 9x^(2)+16y^(2)=144 , are

Draw the graph of the function f(x)=|x^(2)-4|x|+3| and also find the equation f(x)=a has exactly four distinct real roots.

Draw the graph for the lienar equation 3x+4y=12 if x =8 find the value of y with the help of graph

CENGAGE-GRAPHS OF ELEMENTARY FUNCTIONS -Exercise
  1. Draw the graph of y = {{:(2^(x)",",, x^(2)-2x le 0 ),( 1+3.5 x- x^(2),...

    Text Solution

    |

  2. Draw the graph of f(x) = |x-1|+ |2x-3|. Find the range of the functio...

    Text Solution

    |

  3. Draw the graph of y= |x-1|+3|x-2|-5|x-4| and find the values of lamda ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. Find the number of solutions to the question x+log(e)x=0.

    Text Solution

    |

  8. draw the graph of f(x)=x+[x], [.] denotes greatest integer function.

    Text Solution

    |

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

    Text Solution

    |

  10. Draw the region of relation [x][y]= 6, x, y ge 0. Here [*] denotes the...

    Text Solution

    |

  11. Draw the graph of y= {x}^(2), where [*] represents the fractional part...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. Draw the graph of y= -sqrt(x^(2)+2)

    Text Solution

    |

  16. Draw the graph of y= |x|^(1//2) from -1 le x le 1.

    Text Solution

    |

  17. Draw the graph of f(x) = "sgn(log(0.5) x).

    Text Solution

    |

  18. Graph of y= f(x) is given as shown in the following figure. Draw the...

    Text Solution

    |

  19. Draw the graph of the function y= f(x) = lim(n to oo) (x^(2n)-1)/(x^(...

    Text Solution

    |

  20. An even periodic function f:R to R with period 4 is such that f(x)=...

    Text Solution

    |