Math 108-05 Test 2 Review Items

The next test covers Ch 4.1 and 4.2, 5.1, 5.2, 5.3.1, 6.1, 6.2, 6.3, 6.4.

The topics are:

1. Power, root and rational functions—Basic properties, graphs of mother functions and transformations

2. Transformations—Start with the parent function and perform the transformations necessary in order.

Be able to identify a reflection, shift, a stretch or compression by looking at a graph (though being able to produce it yourself is far more important).

A vertical stretch of C > 1 is the same as a horizontal compression 1/C. Vertically the graph stretches by C. Horizontally it compresses by 1/C.

Conversely, a vertical compression of C < 1 is the same as a horizontal stretch C. Vertically the graph compresses by 1/C. Horizontally it stretches by C.

[See Examples 4.2.1 to 4.2.6 and both Comprehension Checks 4.2 and 4.3, posts of solutions, handout]

3. Polynomial functions—Roots, shapes, multiplicities, rational root property. Graphing from these elements as we did on the quiz and in class.

4. Lines (which are polynomials, too)—given two points or a point and slope, find equation of a line (slope-intercept form, point-slope form, distance, midpt, and any other problems in the homework, such as the one about perpendicular bisector nature of line y = x and segment connecting a point on a function with its inverse image point on f inverse.

5. Rational functions—This is Ch 6.1 to 6.4. Monday we will do many graphs of varying levels of difficulty from Sec 6.4.

Know how to graph a function with a slant asymptote, with "holes," with multiple vertical asymptotes, and even ones that intersect their horizontal asymptotes.