Unit+1+Journal

__** Unit 1: Solving/Simplifying/Linear Functions **__

__** 1.1: **__ List the math classes you have taken during high school. Write a few sentences describing your feelings toward math and why - either a good experience or a bad one. Think about what type of learner you are describe the best methods teachers use to help you understand the topics. Please describe your goals after this year - do you need this class to graduate and you are a senior, are you here for MCAS reasons, or what math class or classes do you plan on taking next year?

= Im a Sophore right now, but as a freshman last year i took Geometry Honors, with Ms Kwong. She was a very strict teacher, but she knew how to teach. She was very good at explainning things, and she had many shortcuts to solve problems. Math is my favorite subject. I've liked math ever since i was little. I had a good experience last year learning Geometry. My grades weren't that good, but i still passed the class with a C. The best methods teachers use to help me are by using real life examples. After this year,i plan to take pre-cal. =

__** 1.2: **__
Look at the following, which is an example that has been worked out step by step. Explain in full sentences each step that was taken in the problem and why that step was chosen. Be clear about the step you are looking at, for example "going from line 1 to line 2, ..." All these steps should be written in your online journal. = = = Step 1-2, the equation was multiplied by a common denominator which is 10. = = Step 2-3, everything inside the parenthesis was multiplied by the number outside. = = Step 3-4, 6x was subtracted from both sides. = = Step 4-5, 40 was subtracted from both sides. = = Step 5-6, both sides were divided by -1 which gave the result : x = 60= = Step 6-7, 60 was pluggged in for x to check work. = = Step 7-8, 1/2 and 3/5 were multiplied by 60. = = Step 8-9, 4 was added to 30 and 2 was subtracted from 36, so 34=34. =

__** 1.3: **__
After spending time in class and at home solving a variety of equations, identify the type of problem that is the easiest for you to solve. Also identify the type of problem that you struggle with the most. Why is this type of problem the most challenging? Where do you make your errors most often? What tricks or reminders should you write here (in a different color) as a reminder to prevent that error in the future?

= The type of problem that is the easiest for me to solve is a simple problem such as 7x-3=6x-2. So far i dont' really have a type of problem that i struggle with, but i do make little mistakes here and there that have to do with the signs. For example i'd make a mistake with a problem such as 6(3x-1). I would forget to apply the negative sign and i would make it 18x+6 instead of 18x-6. To prevent this error in the future i should try to slow down the pace at which i work, because sometimes i rush and i make little mistakes like this. =

__** 1.4: **__
List the following words and give a mathematical definition in your own words on your wikispace.


 * Linear Function
 * Relation
 * Domain
 * Range
 * Increasing
 * Decreasing
 * Slope
 * Intercept
 * Degree

= Linear Function- a linear equation or line = = Relation- a relation between mathematical expressions such as equalities or inequalities = = Domain- the set of input values in a function = = Range- the set of all possible values of a function for the values of the variable = = Increasing- when something is being added on to = = Decreasing- when something is being reduced = = Slope- the steepness of a line = = Intercept- the point at which an axis is intersected = = Degree- = = =

__** 1.5: **__
Read pages 67-69 to understand what a relation, linear function, and function notation is then answer the following questions.


 * In your own words describe what a relation is and a linear function is.


 * Give an example of a relation that is a function and a relation that is not a function. Represent the relation graphically and as a set of coordinate points. Explain why your second example is not a function. **__You cannot use example 2 on page 68 as your example.__**


 * Give an example of a linear function written in function notation. Identify the slope and y-intercept of the function. Graph the function and label at least 3 coordinate point that are on the line. **__You cannot use example 4 on page 69 as your example.__**

__** 1.6: **__
Below there is a document which 4 linear graphs shown and 6 linear equations given. In a paragraph, describe how you matched each equation to its matching graph and the order in which you matched them. What graphical features did you look at or which parts of that equation did you focus on?

= First, i matched #2 (2x+4) with graph B, because #1 didn't match with any of the graphs. Next, i matched #6 (-1/2x-4) with Graph C, because #3, #4, or #5 didn't match any of the graphs, so i moved on to the next number. Then, i matched #7 (1/3+4) with graph D. Finally, i matched #8 (-1/3x-4). The graphical features i focused on were the slope and the y-intercept. These helped me to determine which equations went with which graphs. =

__** 1.7: **__
Below there is a document which 4 linear graphs shown and 12 linear equations given. In a paragraph, describe how you matched each equation to its matching graph and the order in which you matched them. Each graph matches one linear function in slope-intercept form and one linear function in standard form There should be two equations per graph. Did you match equivalent functions first or did you try to match each function to a graph first? What graphical features did you look at or which parts of that equation did you focus on?

First, i matched #4 and letter C with Graph A. Next, i matched #1 and letter B with Graph B. Then, i matched #5 and letter A with Graph C. Finally, i matched #3 and letter D with Graph D. First i matched equivalent equations and then i matched each function to a graph. The graphical features and parts of the equations i focused on were the y-intercepts and the slopes. By finding the y-intercepts on the graph, and using the slopes, it was easy for me to determine which functions corresponded to each graph.

__** 1.8: **__
Using the graph below:
 * Complete the following table
 * Write a paragraph describing the walking pattern shown. Use as much detail as possible so that some one would be able to recreate this graph from your description.

Answer the following questions:
 * When is Anne driving the fastest? Explain how you found your answer.
 * What time is Anne stopped? Explain how you found your answer.
 * When is Anne's speed decreasing? Explain how you arrived at your answer.
 * What is Anne's speed at 7 minutes?
 * At what approximate time is Ann driving 35 mph?

__** 1.9: **__
In your classroom binder, title a page "Introduction to Graphical Transformations".


 * Copy f(x) onto the page and create a table of values using x-values 0 through 4.
 * On the right side, sketch a graph and plot each of the five points from your table in a different color.
 * Connect the dots with your pencil to create a linear graph.
 * Back on the left side, copy down g(x) and create a table of values for x-values 1 - 5.
 * On the __**SAME GRAPH**__, plot each of the 4 points from your g(x) table with the same four colors you used before and in the same color order.

f(x)=1/2x

g(x)=1/2(x - 1) + 4