graphing absolute values

Question

graph the following 

 

a) y=|3x-4|

 

b) y=|-2/3x-2|

 

c) y=|-2(x-1)^2+5|

 

d) y=|2(x-3)(x+1)|

Answer 1

Graphing equations with absolute value sign is easy, if you know how to graph the same equation without the absolute value sign. You just flip whatever is below x-axis around x-axis. It's like having x-axis as a mirror for the negative values of the graph.

 

Let me give you an example. How would your plot y=|x-1|

 

First you plot y = x-1, which is a line of slope 1 and x intercept at x=1

so, the line would be on or above x axis for all values of x >= 1

 

For x<1, the line y=x-1 would be below x-axis, so you just flip it around x-axis.

What you get is a line of slope -1 and x intercept at x=1, whose equation would be y=-x+1

 

 

Another tip for you to help plot equations with an absolute value sign is to realize the following:

|-2/3x-2| = |-(2/3x+2)| = |(2/3x+2)| and it's because |-f(x)| = |f(x)|

 

Hope this helps!

 

 

Answer 2

In order to graph absolute value functions, we must understand the concept of absolute values.  If we have a number whether it is positive or negative, the absolute value of that number will ALWAYS be POSITIVE.

 

 

Now we can graph.  Lets chose some values of x that are negative and positive in the interval

 

-2 ≤ x ≤ 2

 

for the first function.

 

a)

 

y = | 3(-2) - 4 |

y = | -10 |

y = 10

 

y = | 3(-1) - 4 |

y = | -7 |

y = 7

 

y = | 3(0) - 4 |

y = | -4 |

y = 4

 

y = | 3(1) - 4 |

y = | -1 |

y = 1

 

y = | 3(2) - 4 |

y = | 2 |

y = 2

 

 

Notice that as the x values increase, the y values decrease then increase.  Also since the absolute value function is a linear type, the graph will have a negative slope from  [-2, 0] and will have a positive slope from [0, 2].  This will construct a positive V-shape graph.

 

 

Do the same to the other functions.  Note that all absolute value function will not look the same due to the type of function we have, if we were to drop the absolute value sign.