A note about translations of functions: I advise my students to determine the horizontal shift the same way you would find x-intercepts, ask "what x-value makes zero?" in the function (in this case, in the absolute value). This prevents problems later when the shift comes from binomials such as (2x-1) or (3-x). If those binomials are in a function, the horizontal shift is +1/2 and +3 respectively, which are the "zeros" of the binomial. "What makes zero?" is a phrase I often use in math classes from Algebra to Calculus.
A note about rational functions: Use the x-intercepts and asymptotes to help choose the correct graph. After simplified, the zeros in the numerator are the x-intercepts and the zeros in the denominator are the vertical asymptotes.
These are perfect for warm-up activities or for part of assessments.
These puzzles were created by combining the instructional method "concept attainment" with an article I read in Mathematics Teacher. Students may not always connect all three ideas simultaneously: function, data, graph. By comparing, contrasting, evaluating, and most importantly connecting these ideas all together, students can build a better comprehension of the functions.
Students will tend not to bridge the connections on their own at first. When introducing the puzzles to students, it is good for teachers (or parents) to ask follow up questions after they correctly group the items. "How do the data points connect to function and the graph?" Once they understand that, then they can double check each placement of the items on their own.
All the activities on this site are made to easily use on Smartboard and touchscreens.