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Looks great, love the connection arrows and your arrangement. 20/20

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Looks great, love the connection arrows and your arrangement. 20/20

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I learned how to apply my knowledge of rational functions to a word problem involving length, width, and perimeter. In the equation of y=24/x, the graph forms to show the relationship between the width and length to form a rectangular figure of 24 tiles. The asymptotes show the requirements that the width and lengths have to be in order to form the dance floor. Another equation of y=2x+2(24/x) explains the relationship between perimeter and length. Again the asymptotes show the restrictions on the value the length can be along with the slant asymptote which shows how the perimeter is larger than twice the length.

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10.) Describe the asymptotes. Explain their meaning.

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10.) Describe the asymptotes. Explain their meaning.

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The vertical asymptote is 0 and the slant asymptote is y=2x. The vertical asymptote is 0 because there has to be an integer for length since it is making rectangular figure, and y=2x because the perimeter will always be more than twice the length since there is also width.

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9.) Write an equation to model this data.

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9.) Write an equation to model this data.

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y=2x+2(24/x)

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8.) Describe patterns in the data and the graph.

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8.) Describe patterns in the data and the graph.

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It has many repeating numbers in the x values. It looks like a rational function. Many of the lengths have the same perimeter.

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7.) Make a table and a graph of Perimeter vs. Length

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7.) Make a table and a graph of Perimeter vs. Length

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x-values = length
y-values = perimeter

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6.) Which design requires the fewest edge pieces? The most?

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6.) Which design requires the fewest edge pieces? The most?

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The design that would require the fewest amount of edge pieces would be 4x6 or 6x4 and the design that would require the most would be 1x24 or 24x1

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If the dance floor was held together with edge pieces...

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If the dance floor was held together with edge pieces...

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Given 24 square tiles that measure 1 meter on each side, a rectangular dance floor must be made.

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1.) Experiment with different rectangles that could be made using all of the tile.

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1.) Experiment with different rectangles that could be made using all of the tile.

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2.) Record your data in a table and on a graph.

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2.) Record your data in a table and on a graph.

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x-values = width
y-values = length

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3.) Look for and describe patterns in the data and the graph.

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3.) Look for and describe patterns in the data and the graph.

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Some patterns I noticed were there's perfect symmetry over the y=x line, the x and y values are interchangeable, and as the width increases the length increases and vice versa.

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4.) Write an equation to model the data.

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4.) Write an equation to model the data.

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y= 24/x

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5.) Give the equation of any asymptotes. Explain their meaning.

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5.) Give the equation of any asymptotes. Explain their meaning.

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y asymptote= 0
x asymptote= 0
There can't be 0 in length or width because that is impossible in a rectangular figure.