Curve Match
Why do this problem?
This challenge could be used as a lesson starter to check students' ability to match curves with their equations. Finding other functions which do not intersect with the existing curves except at the endpoints can help students to develop a stronger sense of how to manipulate functions and the corresponding effect on the graph.
Possible approach
Key questions
Possible extension
Come up with ways of generating curves between any pair on the grid, and prove that there are no intersections except at the end points.
Possible support
Work numerically to plot a few key points for each given function, and use these to identify the $x$ and $y$ axes and each curve.
You may also like
Power Up
Show without recourse to any calculating aid that 7^{1/2} + 7^{1/3} + 7^{1/4} < 7 and 4^{1/2} + 4^{1/3} + 4^{1/4} > 4 . Sketch the graph of f(x) = x^{1/2} + x^{1/3} + x^{1/4} -x