math& 141 precalculus 1 summary portfolio...7 describe how the degree of polynomial affects its...

Math& 141 Precalculus 1

Summary Portfolio

Name:

2

3

Table of Contents

1: The “Toolkit” Functions ......................................................................................................... 5

2: Polynomial Functions…..……………………………………………………..………………………………………..…… 6

3: Rational Functions.. ............................................................................................................ 11

4: Exponential Functions ......................................................................................................... 15

5: Logarithmic Functions ......................................................................................................... 19

6: Representative Functions .................................................................................................... 23

7: Conics ................................................................................................................................. 25

4

5

1: The “Toolkit” Functions Complete the table below.

Function Equation Graph, Domain& Range

Linear

Quadratic

Cubic

Absolute value

Square root

6

2: Polynomial Functions General algebraic form: __________________________________________________ , where

___________________________________________________________________________________________________.

What do all graphs of polynomial functions have in common? What do you know about the domain and range of polynomial functions?

7

Describe how the degree of polynomial affects its graph. In this discussion, be sure to include features such as end behavior, number of maxima, minima, and turning points. Describe how you can analyze the behavior of graphs near the x-intercepts.

8

Algebra skills/techniques essential for understanding and working with polynomials. List all you can think of and how you use them. Give examples of applications of polynomial functions. Give as many as possible.

9

Give examples (at least 2 examples) of polynomial equations and show how you solve them.

10

What are the challenges you faced when studying polynomials? What are areas of improvements and what are the steps you need to take? Describe something about polynomials that you find interesting or fascinating. Are there areas you would like to learn more in depth?

11

3: Rational Functions General algebraic form: __________________________________________________ , where

___________________________________________________________________________________________________.

Describe differences between the graphs of polynomials and the graphs of rational functions. How do the degrees of the numerator and denominator affect the graph?

12

Describe how you find asymptotes for rational functions (horizontal, vertical, slant). In this discussion, include how you determine the behavior of graphs near vertical asymptotes.

13

Algebra skills/techniques essential for understanding and working with rational functions. List all you can think of and how you use them. What are the challenges you faced when studying rational functions? What are areas of improvements and what are the steps you need to take?

14

Describe something about rational functions that you find interesting or fascinating. Are there areas you would like to learn more in depth? Analyze the graph of a rational function below, and determine a possible equation for this function. Explain your reasoning. The graph below has vertical asymptotes, and , and the horizontal asymptote

15

4: Exponential Functions General algebraic form: __________________________________________________ , where

___________________________________________________________________________________________________.

How do the graphs of exponential functions compare to graphs of polynomial and rational functions? What are the distinct characteristics of graphs of exponential functions? Include discussion about important graphical features. How does the base affect the graph?

16

Algebra skills/techniques essential for understanding and working with exponential functions. List all you can think of and how you use them. Give examples of applications of exponential functions. Give as many as possible.

17

Give examples (at least 2 examples) of exponential equations and show how you solve them.

18

What are the challenges you faced when studying exponential functions/equations? What are areas of improvements and what are the steps you need to take? Describe something about exponential functions that you find interesting or fascinating. Are there areas you would like to learn more in depth?

19

5: Logarithmic Functions General algebraic form: __________________________________________________ , where

___________________________________________________________________________________________________.

How do the graphs of logarithmic functions compare to graphs of other types of functions you have studied in this course? What are the distinct characteristics of graphs of logarithmic function? Include discussion about important graphical features. How does the base affect the graph?

20

Algebra skills/techniques essential for understanding and working with logarithmic functions. List all you can think of and how you use them. Give examples of applications of logarithmic functions. Give as many as possible.

21

Give examples (at least 2 examples) of logarithmic equations and show how you solve them.

22

What are the challenges you faced when studying logarithms and logarithmic functions? What are areas of improvements and what are the steps you need to take? Describe something about logarithms or logarithmic functions that you find interesting or fascinating. Are there areas you would like to learn more in depth?

23

6: Representative Functions For each of the 4 types of functions (Polynomial, Rational, Exponential, and Logarithmic), give a representative graph that captures important features of the function. Draw the axes, put scale on each, and label important features clearly. Polynomial Function Equation: __________________________________________ Graph: Rationall Function Equation: __________________________________________ Graph:

24

Exponential Function Equation: __________________________________________ Graph: Logarithmic Function Equation: __________________________________________ Graph:

25

7: Conics Draw two different circles. Give their equations and label their features.

Notes: Draw two different general parabolas. Give their equations and label their features.

26

Notes:

27

Draw two different general ellipses. Give their equations and label their features.

Notes:

28

Draw two different general hyperbolas. Give their equations and label their features.

Notes: