Day: May 14, 2018

Amazon is Taking Over

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The Amazon-ification of Whole Foods

This article is about Amazon’s new branch of delivering grocery items to homes. This article attracted to me because the title simply amazed me. Amazon is the world’s biggest retailer and it is growing at an exponential rate. I had never thought that you would be able to sit at home and not only order your groceries online but also get them delivered to you. Although this new program sounds convenient, I would never use this tool. I do not support this movement because I believe this is going to make the human race lazier and it will prevent face-to-face interactions from occurring. This reminds me of the society in Fahrenheit 451 because they rarely had conversations with others and this movement is a step towards that society. The author explains how Amazon had once before ran “Amazon Fresh” but it went downhill. This gets me wondering how Amazon will be able to pull off this new campaign without shutting it down like “Amazon Fresh”. I do not think that the online grocery store will have the same quality as stores like Superstore or Costco. When you go into a grocery store you get to pick the vegetables that seem fresh and that are in good quality but online you will only be able to select the quantity of food you want. I like how the author, Derek Thompson, has a clear explanation on Amazons plan and includes the future ambitions of the company. At the end of the article, the author talks about how Amazon is planning on creating an online pharmacy and offer healthcare services. By Amazon expanding it’s empire, I think that many businesses will decide to close down and transfer online as well.

Week 13 – Absolute Value And Reciprocal Functions

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This week in Pre-Calculus 11 we started the Absolute Value and Reciprocal Functions unit. This week we learned how to graph an absolute value linear function/quadratic function and we learned about reciprocal functions.

What is an Absolute Value Function? An absolute value function is always in the top half of the graph because the y value has to be positive. Linear absolute value functions make a v-shape and quadratic absolute value functions make a w shape.

Critical Point: The critical point or the point of inflection is where the line or parabola changes direction. The critical point is always the x-intercept.

How To Graph an Absolute Value Function: When graphing an absolute value function it is always useful to graph the original function first. For linear functions, after graphing the original function, you have to look where the line hits the x-axis and then you flip the line by making the slope the opposite.

Ex. y=\mid2x+9\mid

Original Function: y=2x+9

Absolute Value Function: y=\mid2x+9\mid 

y-intercept: (0,9)

x-intercept: (-4.5,0) 

Domain: x\varepsilon\mathbb{R}

Range: y\geq0

Piecewise Notation: f(x)=2x+9,x\geq-4.5

                                 f(x)=-(2x+9),x<-4.5

In the example above, I graphed a linear absolute value function. In the example, as soon as the line hit the x-axis it changed directions. The slope of the original function is \frac{2}{1} but once the line hit the x-axis the slope became \frac{-2}{1}.

Ex. y=\mid x^2-x-6\mid

Original Function: y=x^2-x-6

Absolute Value Function: y=\mid x^2-x-6\mid

y-intercept: (0,6) 

x-intercept: (-2,0) and (3,0) 

Domain: x\varepsilon\mathbb{R}

Range: y\geq0 

Piecewise Notation: f(x):x^2-x-6,x\leq-2 or x\geq3 

f(x):-(x^2-x-6),-2<x<3

In the example above, I graphed a quadratic absolute value function. The first step was to graph the original function. After graphing the original function, I saw where the parabola hit the x-axis and then flipped everything below the x-axis. The original vertex was (0.5,-6.25) but with the absolute value function it turned into (0.5, 6.25) because the y value had to become positive.

 

What is a Reciprocal Function? The reciprocal function of a quadratic or linear function is one over the original function.

Ex. y=x+2

Reciprocal Function: y=\frac{1}{x+2} 

When a reciprocal function is graphed it creates two curves also known as the hyperbolas. The reciprocal of 1 is \frac{1}{1} which equals 1, so it stays the same. Similarly, the reciprocal of -1 is \frac{-1}{1} which equals -1. The points of 1 and -1 on the y-axis are the invariant points (they do not change) these are used to draw the asymptotes. The asymptote is used to separate the hyperbolas. This year, one of the asymptotes is always going to be the x-axis.

Ex. f(x)=3x+4 

f(x)^{-1}=\frac{1}{3x+4} 

 

 

In the example above, the first thing I did was graph the original function. After graphing the original function I found where the line meets at (_, 1) and (_ , -1) to draw my asymptotes. Then I drew my hyperbolas accordingly.