I happened across a review sheet for another instructor’s College Algebra exam today. I know not whose, nor do I wish to know. I just want to use it as an example of what my poor students have to go through.
There were eight tasks on the review sheet. I would like my students to have the skills represented in those tasks for sure. But I wouldn’t happy with just those skills.
So here are the tasks. Each is followed up by the sort of question I would ask my students on an exam. Pity them.
- Original: Find the domain and range of . Follow up: Give two more functions: one that has the same range as f but a different domain, and one that has the same domain as f but a different range.
- Original: Is even or odd or neither. Follow up: Can a function be both?
- Original: Solve the absolute value inequality and graph the solutions. Follow up: How do these solutions relate to the function ?
- Original: Graph the function . Then find the intervals on which f is increasing and decreasing. Are there any local maxima or minima? If yes, where are they located? Follow up: Choose two points near a maximum or minimum value (if such a value exists). Find and comment on the average rate of change between these two points.
- Original: If , find the net change and the average rate of change between and Follow up: Why are these values different? BONUS: Give a new function for which these values are equal between the same two points.
- Original: If , write the transformations that yield . Also graph both and on the same coordinate axes. Follow up: How many solutions are there to this system of equations?
- Original: If and , then what are and ? Also list the domain for each case. Follow up: Choose one of the four functions you wrote. Write its inverse (if such a thing exists).
- Original: Graph this piecewise function Follow up: There is a gap in the graph. Change the second piece of the function to eliminate this gap.