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Absolute Value Functions and Graphs

TopAbsolute value is defined as the value which is equals to both positive value and negative value. Absolute value makes the negative number into a positive number. In absolute value both the real number and its negative have the same value.

An Absolute Value Function graph always made a positive quadrant graph because for all positive or negative values, absolute value function values lie between first and second quadrant.

Now we discuss steps of Graphing absolute value function:
  1. First we put the given value into absolute value function.
  2. After putting the value in absolute value function, we solve the arithmetic operation for the given value.
  3. Then we find the absolute value of the function.
  4. After evaluation of modulus values, now we apply following rules:
⇒ If x > 0, then f(x) > 0 and generated graph made a Point on first quadrant.
⇒ If x < 0, then f(x) > 0 and generated graph made a Point on second quadrant.

Example:

Find the absolute value of 4x for the value x = -2 and graph them for the values x = {-5, -2, 0, 1, 3, 6}

First lets find the absolute value of the function,

f(x) = |4x|
f(-2) = |4(-2)| = |-8| = 8
Now we shall graph the function f(x) = |4x|,
f(-5) = |4(-5)| = |-20| = 20
f(-2) = |4(-2)| = |-8| = 8
f(0) = |4(0)| = |0| = 0
f(1) = |4(1)| = |4| = 4
f(3) = |4(3)| = |12| = 12
f(6) = |4(6)| = |24| = 24
Absolute Value Graph