Parent Function Ideas!

I'm feeling inspired by my teacher friends on Twitter ... they are the BEST of the BEST!

Anyway ... someone on Twitter was asking about Parent Functions.  My activities are "old-school" ... but maybe some of these ideas will inspire creativity in lesson planning.

One of my goals in studying parent functions is to engage students in identifying key characteristics, and then comparing/contrasting the various functions to build fluency with them.

So first we build a parent function "notebook."
Then we identify key characteristics.

Next we compare/contrast.

And last we explore some questions that hopefully get students to thinking!

These activities are online here.

 Possible Synthesis Questions

1. Order the parent functions we are studying from least to greatest by the rate at which f(x) increases as x increases for x > 1.  Explain your thoughts.
2. Use the set of points {(-1,-1), (0,0), (1, 1)} to answer each question.
1. What parent function best describes the set of points?
2. If the points (-2,8) and (2, 8) were added, what parent function would best describe the set?
3. If the point (1, 1) were replaced with (1, -1) what parent function would best describe the set?
4. If the point (-1, -1) were replaced with (4, 2) what parent function would best describe the set?
5. Select 1 or 2 points to change or to add to create a different function than those already described.  Explain your selection and the parent function that would best describe the set.
3. What functions have traits in common? Can you identify a trait that is unique to just one function?
4. Create “Who Am I” Riddles for 5 of the parent functions.  For each riddle use 4 to 6 clues.  Here is an example:  My graph is continuous.  My graph has an intercept at (0,0).  My domain is the set of all nonnegative real numbers.  My range is the set of all nonnegative real numbers.  The shape of my graph is sometimes referred to as an eyebrow.  What parent function am I? (The synthesis questions have been collected over time from various textbooks, activities and such. They are not original with me but I did not keep track of the sources.)

Concept Cards ... sorting can be helpful as students are working out the relationships in parent functions.