Linear


'Absolute Value' is an operator which makes numbers positive. That's all it does. For example, the absolute value of -3 is just 3. If the number is already positive, absolute value does nothing. The absolute value of 5 is still 5.
Mathematically, these statements look like this:   |-3| = 3     and    |5| = 5


We're going to examine what happens to graphs of functions when their equation includes absolute value bars. In other words, what does the graph of   y = -2x + 1 become when you change it to   y = |-2x + 1|?


Let's look at the example mentioned above.


On the right you will see the table of values and graph for the function   y = -2x + 1

This is a linear function. Notice that it does have some negative values, which occur when the value of x is about 0.5, or greater.

When we put absolute value bars on this equation, all those values will become positive. Scroll down to see.





Look what happened to the graph. All we did was make negative numbers positive; we didn't change their value.

So the height of each of the negative points in the original graph remained the same, except up instead of down.

You can also think of this as the line changing direction at x = 0.5, and 'bending upwards'. You can also describe what happened by saying that:
'the negative portion of the original graph got reflected in the X axis'.





... now let's look at a parabola


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