Whits Wacky Graphs EPortfolio

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Whits Wacky GraphsE-Portfolio

• By Student 4
• 7th-Albrecht ?

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Graphing E-Portfolio
Rational Functions
Word Problem
Exponential Function
Absolute Value Function
Technological Tycoon!
Square Root Function
Quadratic Function
Citations
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Quadratic Parent Function yx2

• A parabola is a set of points equally distant
  from a focus and a directrix.
• The general form of a quadratic is y ax2 bx
  c. When you start graphing your equation is y
  a(x h)2 k. The a is the same in both
  equations. You can find your vertex by (h,k)
• For the parent function of a quadratic equation
• Domain (- 8,8)
• Range ( 0,8)

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Graph of Quadratic Parent Function yx2
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Reflection of yx2
y -x2 Domain (-8,8) Range ( -8,0)
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Vertical Shift yx2
y1(x-0)2 4 Domain (- 8, 8) Range (4, 8)
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Horizontal Shift yx2
y(x-4)2 0 Domain (- 8, 8) Range (- 8, 8)
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Graphing Guru of Quadratic Functions

• First, you have to make an x and y chart. Plug in
  an x to find y, then plot the points.
• Make sure to do some negative x points so you
  balance the graph.
• I like to find the vertex from the equation
  first, and then work from there.
• Find axis of symmetry by setting the x value of
  the vertex to x?
• You can tell a lot of things from what a is. For
  instance, if a is negative then the parabola is
  upside down. As a varies the curve changes with
  it.

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Exponential Functiony2x

• An exponential function is when there is a base a
  to the x power, that equals f(x).
• f (x) ax
• Exponential functions are similar to quadratic
  equations because they have exponents. However,
  it is a variable and not a number!
• For the parent function of an exponential
  function
• Domain (- 8,8)
• Range ( 0,8)

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Graph of Exponential Parent Function y2x
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Reflection of y2x
y 2-x Domain (- 8, 8) Range (0, 8)
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Vertical Shift of y2x
y2x 4 Domain (- 8, 8) Range (4, 8)
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Horizontal Shift of y2x
y2 x
y 2(x-4) 0 Domain (- 8, 8) Range (0, 8)
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Graphing Guru for Exponential Functions

• Well, first, you have to make an x and y chart
  like every graph. Plug in a number for x to solve
  for y.
• Now, its important to remember the rules of
  exponents. When it is to a negative power
  remember to put the equation underneath the
  fraction line. Try to have negative and positive
  x-values to best represent the graph.
• It is probably good to know that exponential
  functions start off with very small slope and
  then get bigger as you progress with the graph.
  They grow very quickly so watch out!

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Square Root Function y

• A square root function is the opposite of
  squaring a number.
• y k
• A radical equation is when the unknown variable
  is stuck inside a radical. The square root symbol
  is what makes it radical.
• For the parent function of radical functions
• Domain (0,8)
• Range ( 0,8)

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Graph of Square Root Parent Function y
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Reflection of Square Root Function
y - Domain (0, 8) Range (- 8, 0)
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Horizontal Shift of Square Root Function
y Domain (-4, 8) Range(0, 8)
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Vertical Shift of Square Root Function
y 4 Domain (0, 8) Range (4, 8)
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Graphing Guru for Square Root Functions

• When dealing with square roots, it is important
  to consider the domain first. I say this because
  there cannot be a negative number underneath a
  square root. To find the domain set everything
  underneath the square root equal to zero.
• Next, start to make your x and y chart. Plug in a
  value for x and get y! Make sure to pick a
  widespread of points to get the full effect of
  the graph!

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Absolute Value Function yIxI

• The absolute value is the distance from zero.
• yIx-hI k
• When you take the absolute value of a negative
  number you get a positive number.
• For the parent function of absolute value
  functions
• Domain (-8,8)
• Range ( 0,8)

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Graph of Absolute Value Parent Function yIxI
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Reflection of Absolute Value Function
y-IxI Domain (- 8, 8) Range (-8,0)
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Horizontal Shift of Absolute Value Function
yIx4I 0 Domain (- 8, 8) Range (0, 8)
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Vertical Shift of Absolute Value Function
yIxI 4 Domain (- 8, 8) Range (4, 8)
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Graphing Guru for Absolute Value Functions

• First, you want to make yourself an x and y
  table. Put in your equation the value for x to
  get y.
• I like to find the vertex first. You can do this
  by using the general form of the equation y
  aIx-hIk
• However, it is very important to include negative
  numbers in your chart. You must do this because
  it may be misleading if you only have positive
  points. You could mistake it for a linear
  function when it is not!
• Hint--- if you have a number or from x inside
  the absolute value symbol your graph will have a
  horizontal shift. ( shifts to the left and
  shifts to the left)
• Hint--- if you have a number or outside of
  the absolute value symbol your graph will have a
  vertical shift. ( shifts up and shifts down

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Rational Functiony 1 x

• A rational function is a function of the form
• f(x) p(x)/q(x) q(x)?0
• where p(x) and q(x) are polynomial in x. the
  domain of a rational function consists of the
  values of x for which the denominator q(x) is not
  zero.
• The domain and range for rational parent
  function
• Domain (- 8,0) (0, 8)
• Range (- 8, 0) (0, 8)

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Graph of Rational Parent Function
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Reflection of Rational Function
y1/x Domain (- 8, 0)(0, 8) Range (-8,0)(0, 8)
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Horizontal Shift of Rational Function
y1/(x-4) Domain (- 8, 4)(4, 8) Range (-8,0)(0,
8)
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Vertical Shift of Rational Function
y-4)1/x Domain (- 8, 0)(0, 8) Range (-8,4) (4,
8)
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Graphing Guru for Rational Functions

• When dealing with rational functions, you must
  find the asymptotes and domain. Next, construct a
  table of values, including x-values that are
  close to the asymptotes on the left and on the
  right. Plot the points then draw a smooth curve.
  However, do not connect the two portions of the
  graph, these are the branches.
• An asymptote of a graph is a line to which the
  graph becomes really close as IxI or IyI
  increases without bound.
• The graph has a vertical asymptote at each real
  zero of q(x).
• The graph has, at most, one horizontal asymptote.
• If the degree of p(x) is less than the degree of
  q(x), then the line y0 is a horizontal
  asymptote.
• If the degree of p(x) is equal to the degree of
  q(x), then the line ya/b is a horizontal
  asymptote, where a is the leading coefficient in
  the problem.
• If the degree of p(x) is greater than the degree
  of q(x), then the graph has no horizontal
  asymptote.

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Gravel Falling from Conveyor Belt

• Gravel is falling 4 feet from one conveyor belt
  to another. Because of the way the conveyor belt
  is constructed, the gravel is given a slight
  downward velocity (-1.4 feet per second). How
  long does it take each piece of gravel to fall
  from the upper belt to lower belt?

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Predictions

• Now that I have my equation h-16t2 - 1.4t 4,
  I can solve for whatever I like.
• If it takes two seconds for gravel to fall what
  will the height be, when the initial height is 4?
• First, label what you get from the problem. We
  know that our t.46 seconds. Our initial height
  is s4, and our height is x.
• Now, plug in 2 for t in the equation.
• h-16(2)2 - 1.4(2) 4
• Now, solve for h!
• You should get -62.8 for the height.

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Workin the Wild Word Problem

• First, I wrote down the information given in the
  problem. I first off knew that I was dealing with
  a vertical motion problem. So I had to decide if
  I was going to use h -16t2 s, which is height
  after object is dropped OR h -16t2 vt s,
  which is height after object is thrown.
• hheight (feet)
• ttime in motion (seconds)
• sinitial height (when t0) (feet)
• vinitial velocity (when t0) (feet per second)
• I knew from the information, that this is a
  quadratic function and I would use the quadratic
  formula.
• Next, I wanted to start labeling my information
  in the problem. I knew that the time (t) in
  seconds was my unsolved for variable. I knew my
  initial velocity (v) was -1.4 feet per second,
  and I knew my initial height (s) is 4 feet. I
  know the height (h) is 0 feet. I then made an
  equation out of this known information. 0 -16t2
  - 1.4t 4. to solve for t, I needed to put it
  into standard quadratic equation which is ax2
  bx c 0. So, I had -16t2 -1.4t 4 0. After I
  had my equation, I labeled my a, b, and c. a -16
  b -1.4 c 4. I put those terms in the quadratic
  formula. b plus or minus the square root of b
  squared minus 4ac all over 2a. I solved for t and
  got approximately .46 feet per second!

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Graph of Word Problem
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!Technological Tycoon!

• Okay, I have come up with some useful hints for
  those technologically
• challenged or just plain confused. ) Good luck!
  I Hope you enjoy graphing just as much as I do!
• Sometimes these problems can get pretty
  difficult, so I like to put my equation in the
  y1 screen by going to the y button in the top
  left corner of my calculator. After that, I hit
  graph. I then go to 2nd (the button underneath
  the y) and then table (which is the graph
  button). This gives you a table of values to get
  a general idea of where the points are located on
  your particular graph.
• To find the absolute value symbol 2nd CATALOG,
  and its the first one!
• Now, say you want to find a specific value. You
  can go to 2nd and then trace (the button next to
  graph button) and hit 1. This will make x__ pop
  up on your graph screen. You can then put in a
  value of any x to find what y is at that point!
• If you have graphed a graph and it is not showing
  up try adjusting your window by WINDOW, then you
  can change your Xmin, Xmax, Ymin, and Ymax to
  match the scale of your graph, press graph and
  your graph with you new window scales should show
  up.
• Lastly, it may be helpful to find your zeros in
  some functions. So, after you graph your equation
  go to 2nd, trace, then hit 2. Then use the arrows
  to navigate and find your zeros!

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Citations

• Hart-Davis, Damon. "Textures and Surfaces." DHD
  Multimedia Gallery. 1997. 30 Apr. 2006
  lthttp//gallery.hd.org/_c/textures/_more2000/_more
  10/gravel-1-BRM.jpg.htmlgt.
• Hoefler, Jonathan, and Tobias Frere-Jones.
  "Numbers Overview." Hoefler and Frere-Jones. 30
  Apr. 2006 lthttp//www.typography.com/catalog/numbe
  rs/images/Overview_Numbers1.gifgt.
• "Index of/Images." Science Line. 2004. Science
  Line. 27 Apr. 2006 lthttp//www.scienceline.net/ima
  ges/i20love20math.JPGgt.
• Larson, Roland E., Timothy D. Kanold, and Lee
  Stiff. Algebra 2 An Integrated Approach.
  Evanston D.C. Heath and Company, 1998. 2-944.
• "Sliding Belt Conveyors." Bollegraaf Recycling
  Machinery. 2002. 30 Apr. 2006 lthttp//www.bollegra
  af.com/images/glij-2.gifgt.
• Stapel, Elizabeth. "Need Help with Algebra?
  Youve Found the Right Place!" Purplemath. 1998.
  18 Apr. 2006 ltwww.purplemath.comgt.
• .
• Whatis.Com. 2000. TechTarget. 19 Apr. 2006
  lthttp//whatis.techtarget.comgt.

VanMullen, Greg. "Math GV Function Plotting
Software." MathGV. February 16,2002. April 2006
lthttp//www.mathgv.com/gt.