Desmos Art Function Card 2018

When I was trying to figure out equations for this project I used my understanding from previous units to remember the equations. I also had to look back at the book and experiment with equations that I forgot could work on my card. In some cases I could use multiple equations for certain pieces on my card and it was challenging to figure out which equation would be best for the job based on the different qualities of them. For me it was hard to figure out how to shade in my self portrait, I had to change many of my equations so that I could be able to shade certain parts. Another challenge was to use a rational function, because I had completely forgot about them. I ended up adding two of them in on the center of my reel. I got help from some of my friends in different classes, since we did the project during the break. One of my friends gave me the idea for my card while we were going to the store to get some ice fishing gear together. A strategy that I used was giving all of the functions individual names so that I could use the names to shade in parts of my card. This holiday card helped me become more efficient, because had to input so many different transformations, functions, and relations, and this made me memorize how they all looked and what I needed to reflect or translate the functions into what I wanted.

What Darwin Never Knew

Charles Darwin published the book “On the Origin of Species” in 1859 where he developed the theory of evolution, by natural selection. There has been lots of controversy surrounding Darwin’s theory of evolution, however through the discoveries of DNA and fossils Darwin’s theories have proven correct. Natural selection is the process, by which organisms change over time as a result of behavioral and physical traits. These changes will allow an organism to better adapt to the specific environment it lives in. The organism will be better fit in its environment to allow it to better survive and reproduce. Being fit does not mean strong or conditioned, it means fitting into the surroundings which an organism lives into better. The variations of organisms will allow the better fit to live, while the unfit will die.

Darwin observed the process of evolution, but he did not understand the mechanism by which it was being performed. The discovery of DNA and how they are passed down from parent to offspring explained this. The genes that are in the DNA passed down from parents, is what gives the offspring their certain traits. Although the genes are very similar they do not stay the same. The DNA gets changed from mutation, which is an error in the coding of DNA. Mutations can be harmful or neutral to an organism, but there are rare cases where they can be beneficial. When they are beneficial this gene gets spread throughout the population and that is what guides natural selection. This proved Darwin’s theory correct.

An example of this would be a rat getting a mutation to have a darker coluored body. If the environment the rat lived in was a darker coluor the rat would be able to camouflage himself into his surroundings better than the lighter coloured rat. This mutation would be beneficial to the rat and allow him to survive and reproduce, while the rats without the mutation will die off and this is natural selection. The environment an organism lives in is always changing, so these mutations allow an organism to survive and adapt to the constantly changing environment around it.












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Week 18 – Top 5 things I learned in Pre-Calculus 11

1.  How to understand and solve word problems.

Learning how to solve word problems is very important to me, because these are most of the problems that I will face in everyday life. It is a good skill to have and will help me in the future. This is an example of a problem I may face if I went into business.

2.  Graphing

Graphing is a good skill to know, because is helps understand and analyze data. I have learned that there is so many different ways you can graph and so many different types of data you can graph. Graphs, also are displayed to me very often in life. Some important terms are the roots, y intercept, slope and the vertex. Here is a graph showing the power and torque curve on a miata.

3. Inequalities

Inequalities are used with limits and they can telll you the limits of what you can make, build, buy etc. I learned how to solve inequalities by factoring. Inequalities can also be plotted on a graph. This is a question about the max food you can buy for $5 and I think this is a very important skill to know.

4. Solving expressions

Solving expressions were involved in about half of our units. I learned how to solve expressions in many different ways, for example factoring, completing the square, graphing and the quadratic formula. All these methods work for different expressions. Here is an example of factoring and completing the square to solve the same expression.

5. Trigonometry

Trigonometry was a very interesting unit. The relationships from the sides and angles in a triangle can help you solve many different problems involving shapes and direction. You could use trigonometry in carpentry, geography and navigation. Here is a common question that I learned how to do.

Week 17 – Angles in Standard Position

This week I learned about angles in standard position.

Here is a common question:

This question first asked me to graph point P in standard position. I did this by using the x value 11 and y value -7, and then connected the lines to create a right triangle. The next question asked me to determine the primary trigonometric ratios of theta, so then I had to find the missing side length r by using pythagoras theorem. After I had all the side lengths of the triangle I could plug them into sin y/r cos x/r and tan y/x. The last question asked me to figure out what theta was. First I used tan to get the reference angle, and then I subtracted 360° to get the rotation angle.

This week we also learned the sine law and the cosine law. You can use the sine law when you have an angle that is across from a side length. For the sine law you also have to use the cast rule to figure out if there is an ambiguous angle. You can use the cosine law when you have two side length and one angle or all three side lengths.

Week 16 – Solving Rational Equations

This week I learned how to solve rational equations.

Here is a common question:

This question asked me to solve the equation. The first step was to find a common denominator. Then I multiplyed the common denominator by both numerators where that part of the expression was already there. After I just had to solve and find the non-permmisble values.

Week 15 – Multiplying Rational Expressions

This week I learned how to multiply rational expressions.

Here is a common question:

This question asked me to simplify the expression. The first thing i did in this question was reduce the coefficients, and then I combined the two expressions together since it was multiplying. After I factored out what I could from the expression to figure out which factors can cancel out. Then i just reduced a to figure out my answer. The last step was to find out the non-permissible for a, and this means the values that will not make the denominator equal to zero. This is because in a division question you aren’t allowed to have the denominator  equal to zero.

Week 14 – Graphing Reciprocals of Quadratic Functions

This week I learned how to graph quadratic reciprocal functions.

Here is a common question:

This question asked me to figure out the parent function of the graph. I knew it was c, because I drew the parent graph by going through the invariant points. I also knew that the graph only had one root, because there was only two hyperbolas. Then I used 1,3,5 to draw the rest of the graph.

Week 13 – Graphing Reciprocal Linear Functions

This week I learned how to graph linear reciprocal functions.

Here is a common question:

This question asked me for each pair of functions, use the graph of the linear function to sketch a graph of the reciprocal function, and state the domain and range. First I sketched y = x + 2 by using the slope and the y intercept. Then i had to sketch the reciprocal of that function. First I figured out where the invariant points so I could draw the vertical and horizontal asymptotes. The graph never cross the asymptotes. Then I could sketch in the reciprocal of the graph. The domain and range are both elements of the real numbers, but they do not go through the origin of the graph, because there is no reciprocal for 0.