# Shifting of a Graph

To know how a graph would shift, we need to know two things:

- The shifting is either on the X-axis or on the Y-axis or on both of them,
- The shifting is in the +ve direction or in the â€“ve direction.

Let us understand this phenomena with the help of an example

*y*=*f*(*x*) = |*x*|

# Case 1

If y = f(x) is changed to |
Impact on the graph of y = f(x) |

Y = f(x) â€“ 5 |
It will shift 5 units downwards, i.e., 5 units on the â€“ve Y axis |

*y*= |

*x*| âˆ’ 5

# Case 2

If y = f(x) is changed to |
Impact on the graph of y = f(x) |

Y = f(x) + 5 |
It will shift 5 units upwards, i.e., 5 units on the +ve Y axis |

â€‹

*y*= |

*x*| + 5

# Case 3

If y = f(x) is changed to |
Impact on the graph of y = f(x) |

Y = f(x) âˆ’5 |
It will shift 5 units rightwards, i.e., 5 units on the +ve X axis |

â€‹

â€‹

*y*= |

*x*âˆ’ 5|

# Case 4

If y = f(x) is changed to |
Impact on the graph of y = f(x) |

Y = f(x) âˆ’5 |
It will shift 5 units leftwards, i.e., 5 units on the +ve X axis |

â€‹

â€‹

*y*= |

*x*+ 5|

# Case 5

If y = f(x) is changed to |
Impact on the graph of y = f(x) |

Y = âˆ’f(x) |
It will be reflected along the X-axis as if X-axis is a mirror |

â€‹

â€‹

*y*= âˆ’ |

*x*|

# Case 6

If y = f(x) is changed to |
Impact on the graph of y = f(x) |

Y = |f(x)| |
Graph below the X-axis will be reflected along the X-axis on its above as if X-axis is a mirror |

â€‹

We can summarize the whole phenomena of the shifting of a graph as:

We can summarize the whole phenomena of the shifting of a graph as:

- If there is a change in the value of X-axis, then it will move on the X-axis and similarly for the Y-axis. The graph of y =
*f*(*x*âˆ’5) has a change in the values of*x*where as graph of y =*f*(*x*) â€“ 5, which can be written as y + 5 =*f*(*x*) has a change in the values of y. - If there is an addition, then the graph will move on the âˆ’ve side, either on the X-axis or on the Y-axis and if there is a subtraction, then graph will move on the +ve side.

Example

The graph of

*y*= |*x*| is given. Draw the graph of*y*= ||*x*|âˆ’2|.Solution

Let us first sketch |

*x*|âˆ’2.Now ||

*x*|âˆ’2| will be having all the negative part of |*x*| âˆ’2 on the positive side of Y axis, or above X-axis.