ShmoopTube

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Here's your shmoop du jour...

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Which equation matches this graph?

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Here are the choices...

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First of all, it seems like we have a cosine graph...

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It's cut unevenly by the x axis.

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The bottom part of the graph only seems to go down to negative 1, while

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the top parts reach all the way up to positive 3.

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A normal cosine graph goes up and down in even amounts relative to the x-axis, which

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means that this one is lifted up by 1...

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...in other words, if we bring the graph down by 1, it will reach both 2 and negative 2.

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The "lift" is represented by a "plus 1" which leaves only

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answer choices D and E in the running.

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place that pesky 2 -- before or inside of the parentheses?

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We know that anything inside the parentheses modifies the period of the graph, or how tightly

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the waves of the graph cycle. A normal cosine graph completes a full cycle

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in 2π, and our cosine graph does the same, so it was not modified.

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That means the 2 can't be in the parentheses but rather before the cos -- answer E.

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