Graphing Absolute Value Functions

Warm-up  

Constant function f(x)= ANY NUMBER

Identity function f(x)=x

Absolute Value Function Formula y = A|x-B|+C When using this formula, the vertex point of an absolute value function is (B, C). B is the movement left or right C is the movement up and down

If A is between -1 and 1 (not 0) the function will be WIDER than the parent function this is a vertical Shrink If A is greater than 1 or less than -1 the function will be NARROWER than the parent function this is a vertical stretch. If A is positive the graph opens up If A is negative the graph opens down

Find the vertex point of these absolute value functions: y = 3|x-6|+5 y = -2|x+4|-7 y = |-x|+2 y = |-x-1| y = |x| (6, 5) (-4, -7) (0, 2) (1, 0) (0, 0)

Graphing with a Table: (4, 2) Graph the function: y = 2|x-4|+2 Step 1: Find the vertex point. Step 2: Make a table where the vertex point is the middle value. Step 3: Fill in the table. Step 4: Plot the points. (4, 2) X Y 2 2|2-4|+2 = 6 3 2|3-4|+2 = 4 4 5 2|5-4|+2 = 4 6 2|6-4|+2 = 6

Graphing with the equation Graph the function: y = 3|x+1|-4 Step 1: Find the vertex point. Step 2: Plot the vertex point. Step 3: Use “m” of the equation to move to the next point. Step 4: Go back to the vertex point. Step 5: Use “-m” of the equation to move to the next point. Step 6: Connect the dots. (-1, -4)

Label the vertex Label 5 points   Label the vertex Label 5 points Determine the transformations from the parent function? (up,down,right or left)