Chapter One Study Guide Name______

Pre-CalculusL32016-2017

Chapter One Study Guide Name______

This chapter “sets the stage” for the functional analysis we do in this course. For the rest of the year we apply what we learned in this chapter to different functions. 86 weighted points

You will create a study guide of problems drawing from homework, notes and quizzes. This study guide will be completed on separate paperwith work shown clearly and completely. It’s always a good idea to write a few notes amongst your work to further solidify your understanding. Please attach this sheet as your “cover sheet” (and scoring rubric). Your study guide is due on the day of the test – NO late study guides accepted (what’s the point of doing all that work after the test?).

***Items with asterisks will be in the “no calculator” portion of the test.

1)***12 Basic Functions – Identify graph types (parents)and answer questions about the basic functions (see page 113 #1-18 for problem types).

1. For the study guide you will draw a thumbnail sketch of each of the basic function graphs & the equation for that function. Also make a note of a particular property that might be significant for each function. (Like asymptotes, or some restricted domain or range or something with continuity or boundedness. The only boring one is the linear/identity function). 12 points

2)Properties of Functions – Analyze functions by examining and describing a variety of characteristics.

1. Do a full analysis on the function f(x) = -0.2x4 – x3 + 3x2 – 5 (see p 22 of ISN for analysis points) 12 points
2. Show the variety of asymptotes possible in functions by providing the following examples. Support each with a graph and by identifying all asymptotes, domain, range & continuity (or discontinuity). 8 points
3. Exponential function with HA ≠ 0
4. Rational function with slant asymptote
5. Rational function with hole
6. Rational function with two VA
7. Do a full analysis on a piecewise function – be clear about point(s) of discontinuity

2 points

1. State and verify even-odd-neither of a function algebraically by working through one example of each showing a clear algebraic proof for each. 3 points

3)Modeling with Functions – Students will be able to solve problems similar to those we worked on in class. 5 points

1. You will do a multi-step modeling problem – it is suggested you work through the quiz problem or do a three-dimensional situation (such as the box problem or the problem noted below). Do three things with this problem (1) write an algebraic model for the scenario (2) draw the graph of the problem situation and (3) Answer a question about the situation (such as maximum area or volume and dimensions that result in that). 4 points
2. Also look up & write the definition of girth of a box and make sure you can use the definition in a problem. 1 point

4)***Transformations of Functions – Students will be able to identify transformations given an equation (and draw graphs of both the parent function & transformed function, following pre-determined points from the parent)Students will be able to write a new function equation given a list of transformations performed on one of the basic functions.

1. Use a transformed function such as exponential, logarithmic or square root (at least 4 transformations) – identify the parent with a functional equation, name the transformations, make a general formula for any ordered pair of the transformed function and identify three points from parent to new. Draw a graph of both the parent & the transformed function, using your transformed points (without using a calculator). 9 points
2. You will take a list of transformations (be sure to write out the list – see p 37 of ISN) and write the function equation that results from applying those transformations to the parent function. 3 points

5)Composition of Functions – Students will be able to give a new function equation for a composition of two functions, and be able to identify the new domain finding all holes including any hidden ones.

1. You will work through an example of a composition of a pairof rational functions, identifying the domain of the resulting composition. 5 points
2. You will decompose twodifferentfunctions into their pre-composition parts.

4 points

6)Inverse Functions – Students will be able to find the inverse equation of a function and identify the (possibly restricted) domain of inverse.

1. You will find the inverse of the following two different types of function equations. You will clearly name the inverse function equation (with inverse function notation) and the domain and range of each. Also make a rough sketch of the original and inverse (can graph on calculator and copy your sketch from there) showing how they reflect over the line y = x.
2. Original is either quadratic or square root (be sure it is not the pure parent)
3. Original is a rational function8 points

7)More Problem Solving – you should be able to work with applications of certain function types 6 points

1. Work through an inverse function application. Be sure to quote the problem and show all work. See page 137 #47 or class examples 2 points
2. Work through a logistics word problem. Be sure to quote the problem and show all work. See page 285 example 8 or p 298 #45 2 points

Your studying should include going over any homework problems that you have been assigned this chapter, reviewing all your class notes, going over previous quizzes and completing the study guide detailed above