Piecewise functions 9-20 class notes

Homework for 9-21 is page 25, items a, b, 7 and 8.

Yesterday and today we used easy, integer x's as inputs for a table of values for a piecewise function.  When an x makes a condition true, you use the associated rule to obtain the function or y- value.

If the condition has a "<" or ">" inequality without an equal sign, the graph of that piece will have an open dot at the end of the line, meaning you can't use the x-value for that position to create a y-value.  That piece of the function has no value, no x, no y, no orederd pair at that position.

If the condition has a "<" or ">" inequality including an equal sign, the graph of that piece will have a closed dot at the end of the line, meaning you use the x-value for that position to create a y-value.  That piece of the function has a definite value and ordered pair at that position.

When we make a table of values, we use integers so it's easier to plot the points on a grid.  When we connect the points with a line, it means there are many points besides our easy integers which satisfy the expression and the condition.  The domain and range of a function piece that is a line can have fraction and rational values, numbers in between the integers.  The domain and range are not limited to integers or easy points.  In item 5, the domain is "x is all real numbers", and the range is "y is all real numbers > 0."

We discussed why the graphs of piecewise functions look strange.  We are familiar with functions having a single rule, or expression, and one or no restrictions (conditions).  Each piece of a piecewise function can have a different shape: Two straight lines with different slopes, or a curve and a straight line.

Homework for 9-21 is page 25, items a, b, 7 and 8.

Quiz preparation:

Given the graph of a piecewise function, state the domain and range.

Given the expressions for a piecewise function, make a table of values and draw a graph.

Write a description of a piecewise function, describing where it changes from one piece to another, what the shapes of the pieces are, and what the domain and range are.