## A recurring strand in Exeter's math curriculum

Transformations arise in a variety of settings throughout our problem sets. Here are a few examples.

**Math 1**: Graph *y *= |*x*−5| and *y *= |*x*+3|, then describe in general terms how the graph of *y *= |*x*| is transformed to produce the graph of *y *= |*x*−*h*|.

(Math 1, #309)

**Math 2**: Apply*T*(*x*,*y*) = (2*x*/3, 2*y*/3) to the following pentagons:

- vertices (3, −3), (3, 3), (0, 6), (−3, 3), and (−3, −3);
- vertices (15, 0), (15, 6), (12, 9), (9, 6), and (9, 0). Are the results what you expected?

(Math 2, 54#6)

**Math 3**: Describe the effect of each of the following geometric transformations. To generate and test your hypotheses, transform some simple points.

(a) *T*(*x*,*y*) = (−3*x*, −3*y*)

(b) *T*(*x*,*y*) = (−*y*,*x*)

(c) *T*(*x*,*y*) = (−*y*, −*x*)

(d) *T*(*x*,*y*) = (0.6*x*− 0.8*y*, 0.8*x*+ 0.6*y*)

(Math 3, 16#6)

**Math 4**: The slope of the curve *y*= 2*x *at its *y*-intercept is ln(2), which is approximately 0.693. Use this information (but no calculator) to find the slope of the curve *y*= 3 2*x *at its *y*-intercept. Answer the same question for *y*= 23 2*x*, then use your result to find the slope of the curve *y*= 2*x *at the point (3, 8).

(Math 4, 20#6)

Other strands that arise throughout our problem sets: