How To Find and Graph the Inverse of a Function

In this video Algebra 2 Math Lesson, I model how to graph a quadratic function and its inverse. The process starts with graphing a parabola in the form y=a^2+c. The vertex is given by (0,c). After graphing the parabola with four additional points, I create the inverse’s graph by moving the points about y = x line. Finally, I find the inverse of the original function.

If this video math lesson on finding the inverse of a function and then graphing it helped you, leave a comment. Heck, if it didn’t help leave a comment and let me know how to make it better.

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Algebra 2 Chapter 7 Practice Test Answer Key

This post is primarily for my Algebra 2 students. It is the Answer Key to the Chapter 7 test on Radical Functions and Rational Exponents.

Topics of the test include: roots and radical expressions, multiplying and dividing radical expressions, binomial radical expressions, rational exponents, solving square root and other radical equations, function operations and inverse relations and functions.

The file below contains the work I would show to solve the problems and it is in pdf format. If you have any questions, use the comment section to post them.

Algebra 2 Chapter 7 Practice Test Answer Key

Regards,

Mr. Pi

How to Find the Inverse of a Relation and an Equation

This video lesson covers the definition of the inverse of a relation and reviews the concept of how to find the inverse of a relation.

Example 1 covers how to find the inverse of a relation from a table of values and provides a good visual of a relation that is a function and its inverse is not a function.

Before example 2, a discussion about how switching the x and the y in the equation is the best method for finding the inverse of a function. Example 2 models how to use the x and y switcheroo to find the inverse of a given function.

Meta Congition Assignment

Below is a bonus assignment that I post on my fan page on facebook. At the time of this post, I have 32 fans and about 6 of them are family and friends, so I have about 26 student fans. I received four completed assignments. It is good for me because I have less to read over, but not good for the students because not all students “have a facebook” . So, if you are a student without a facebook and want to complete this assignment then here is your chance. It is due Thursday, March 25, 2010.

This is designed to get you thinking about your thinking.

Part 1 – Google search –> “thinking about how you think” meta cognition and read up on meta cognition
Be sure to use the quotes when you google search.

Part 2 – Go to this link http://wp.me/pEaoO-7j and read the post

Part 3 – Respond to following questions:

How will using an instructional tool like a pretest help me prepare for the exam? How will the using the pretest hurt me in the long run?
How does this information help my teacher help me?

If you are in algebra 2, respond to this question: Do I really need a pretest to help me prepare for a test?

If you are in geometry, Do you think this pretest is a good or a bad idea? Explain why.

You can email me at school address or you can type it up for me and turn it in on Monday, March 22, 2010. You must answer all the questions with at least one sentence. Not using a sentence means you will receive credit.

Do not ask me what my school email address, I will not put that on facebook. I do not want any school information shared on facebook.

Regards,

Mr. Pi

Look for an upcoming article on my thoughts on bonus work.

How To Simplify Rational Exponents

This lesson covers how to simplify rational exponents in exponent form using the properties of exponents and is the second part to my blog post on Radical Form and Rational Exponents. Working with rational is an algebra 2, but the properties of exponents learned in algebra 1 with integer exponents apply. Here is a list of the properties of exponents for review:

  • Product of Powers  a^{m} \cdot a^{n} = a^{m+n}
  • Power of Powers   (a^{m})^{n} = a^{mn}
  • Power of a Monomial (ab)^{m} = a^{m}b^{m}
  • Negative Exponent a^{-n} = \frac{1}{a^{n}}
  • Quotient of Powers \frac{a^{m}}{a^{n}} = a^{m-n}
  • Power of a Quotient  (\frac{a}{b})^m = \frac{a^{m}}{b^{m}}

The first section of the video reviews the above list of properties.

The second part of the video (example 4T part a) simplifying the expression (-32)^{\frac{3}{5}}. There are two methods to simplify this expression. The first method that is modeled is using the properties of exponents and the second method modeled is converting the rational exponent into a radical and a power. Either method that is used requires the problem solver to figure out “what number can be raised to the n power to get the original number?”

Example 4T part b is similar to part a, but the exponent is expressed as a mixed decimal number. To evaluate this expression, the mixed decimal number needs to be converted to an improper fraction. Then either method modeled in part a can be applied.

Finally, example 5T involve a more complicated expression to simplify and it involves negative exponents. The key concept to know is that all negative exponents need to be expressed as positive exponents.

Enjoy the video and feel free to post any questions in the comment section.

Regards,

Mr. Pi

What Is The Purpose of a Pretest in Geometry?

If you are my student and want a copy of the chapter ten geometry pretest click here. It will open in a new window and it is in pdf format.

I have not used this blog to discuss my thoughts on education and I am not sure if I am ready to blog about all of my views on education, but I have many thoughts on my mind as this school year continues.

My geometry students have not been performing as well as expected on the past two chapter exams, the averages are lower than the previous exams. The main factor for this is because of the type of assessment. The last two chapter tests consisted of 17 multiple choice questions and 2 open ended questions. The set up is similar to the state assessment test and I have changed to this type of assessment to give my students practice taking the state exam. Even my best students get fooled by the trick answers on the multiple choice section. The evidence = lower test scores. My students do well on the open ended questions, but get destroyed on the multiple choice section.

Prior to these chapter tests, all of the questions on chapter tests were open response. Open response questions are more forgiving than a multiple choice question, because of partial credit.  To review for the test I used two class periods one day to complete the review in class. The assignment was to finish the practice for discussion the next day. The review was a practice test and it had the same types of problems on the chapter test except the problems will be in a different order, the answers will be in a different order and different numbers will be used. The second day I provided the answers and modeled any question on the board if a student asked. I spent the entire period doing problems on the board.

A two-thirds majority (32/48 = 67%) stated I did everything I could to prepare them for the test and a lack of studying on their part caused the lower test score. Along with these admissions, there were some very good suggestions:

  • Review games x 3
  • Complete the review problems as a class
  • Having more examples of each problem x 4
  • Along with the answer key on the blog, show a walk through with the multiple choice problems
  • Go over the review more thoroughly
  • Time before the test to ask questions
  • Go over the open ended questions x 2
  • Go over the theorems and postulates more
  • Going over the homework more
  • Criticized me homework policy

I took a few days to think about how to rise to this challenge to improve my student’s achievement. I decided to use a formative assessment prior to the start of the next chapter. I created and administered a pretest in geometry class. Here are the results of the pretest multiple choice section:

Chapter 10 Geometry Pretest Results

Chapter 10 Geometry Pretest Results

I shared the results with my students before the starting the first lesson and explained the set up of the test. It was made clear that the test will be similar. The key differences are the problems will be in a different order, the answers will be in a different order and different numbers will be used. Other than that, the problems are the same. The core of the problem remains intact. I also pointed out that this pretest will be used as a teaching tool to help drive the instruction.

During the first lesson, the students used two handouts: a copy of the geometry pretest and a copy of the guided notes. The first problem was finding the area of a parallelogram and most students got the first problem correct, I quickly showed them the first teacher example and the students completed the next example individually and used the solve pair share technique. It was a nice easy example to set the learning mood and it provided an opportunity to introduce the parts of a parallelogram and introduce the pretest as a learning tool.  At the conclusion of the first two examples, I pointed out that is what the first question on the test is assessing.

The second example was finding the missing height of a parallelogram when the area, the lengths of both bases and the other height is given. Even though this problem is not on the end of chapter exam, it is something neat to discuss and learn. Again, I modeled an example and the students completed the an example using the solve pair share technique.

Similar to the first example, the third example reviewed finding the area of a triangle. As in the first two examples, I modeled an example and I modeled an example and the students completed the an example using the solve pair share technique.

The fourth example required the use of a formula to find the force wind creates when blowing across front or rear face of a barn. Without getting into too much detail, the students got this problem wrong on the practice test because the correct answer is supposed to be in tons, but most of them found the answer in pounds. I do not even need to ask if the problem looked familiar. Most of them reached for their pretest. They see the pretest as a learning tool by the end of the first lesson, sweet! As I did my example, I was given help from students finishing my sentences until we got to the conversion, then everyone became quiet and paid attention. I modeled how to convert pounds to tons using a ratio. For their example, they had to find the answer to the practice test question.

As I revealed the assignment problems, I related the other two test questions from that section to the problems from the assignment. I gave a verbal description on how to do both problems before the students were dismissed. I can not wait until to see the assignments and test results.

Until next time,

Mr. Pi

Rational Exponents and Radical Form

This video math lesson introduces the connection between radical form and rational exponents. The first example establishes the connection between the index and the denominator. It models evaluation three real number expressions.

The definition of Rational Exponents in Radical Form is explored and example two should help in reinforcing the fact that the numerator is determines the power and the denominator determines the index.

Example 3 is a word problem. As many of my students in class complained or should I say, voiced their concern over covering a word problem. It is just an application of a known equation with two variables. You have to two things

1. Identify what you must find
2. Identify what you are given

Once you do that it is quite easy. You will see in the video. Enjoy.

Follow this link to read and watch more about rational exponents.

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