Precalculus Test Review
Ch. 3.1-3.6
Be able to:
- Explain the difference between point symmetry and line symmetry.
- Determine if a function is symmetric with respect to the origin, the x-axis, the y-axis, the line y = x, or the line y = -x when given an equation or a graph.
- Explain what it means for a function to be even or odd.
- Graph the basic “parent” graphs of functions. (p. 137)
- Graph changes to parent graphs based on an equation of a function. (table on p. 139-140 and that quiz we took).
- Describe how two graphs are related when given their equations (e.g. shifted up 2 units, or f(x) is the reflection of g(x) across the y-axis).
- Shade appropriately on a graph when given an inequality. (We skipped this section because we already knew how to do it. See examples 2 and 3 from p. 146-147).
- Describe a function and its inverse using tables, graphs, and equations.
- Show that two relations are inverses by using the compositions f(f-1(x))and
f-1(f(x)) to arrive at the identity function. - Describe different types of discontinuities.
- Show that a function is continuous at a point using the continuity test.
- Describe the end behavior of a function.
- Describe intervals over which a function is increasing and decreasing.
- Determine if a function value at a given critical point is a maximum, minimum, or a point of inflection.
- Determine relative and absolute extrema of a given function.
- Explain what a critical point is. (something about tangent lines)
I recommend that you work the following problems in addition to studying the above topics. I will answer any questions that you have about the above topics and the recommended problems below on the day before the test. IF YOU DO NOT HAVE QUESTIONS ABOUT THIS MATERIAL I WILL MOVE ONTO NEW MATERIAL ON REVIEW DAY.
- P. 197 #’s 1, 2, 3, 5
- P. 198-199 #’s 11-18, 19-21, 23, 24, 29-34, 35-47