Transformations of Functions

The easy translations

The difficult translation


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Weekly Reflection 9-14-18

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Trigonometric Word Problems: I will be able to find trigonometric ratios of acute angles. One example of a trigonometric word problem is: A 15 foot ladder rests against a tree on level ground and forms a 75 degree angle of elevation. What is the height of the tree? What is the distance of the tree to the base of the ladder. The first step in solving this problem would be to go through and find any important information. I know that the ladder leaning against the tree forms a right angle so I will be using a trig ratio. The ladder is 15 feet long and is the hypotenuse so I have one length. The ground under the tree forms a 75 degree angle of elevation. This angle is across from the 90 degree angle. To solve this problem I need to find height and the base of the tree from the ladder. To find height I need to find the Sine (opposite over hypotenuse) 75 degrees = x/15. If I multiply 15 to both sides I can cross out the 15 in the denominator: 15(sin75)=x, x is approximately 14.49...
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Weekly Reflection 11-2-18

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Writing Piecewise Functions: I will be able to write piecewise functions. An example of writing piecewise functions: In order to write a piecewise function the first thing I look at the higher function and figure out if the function goes on forever or has a ending point. The top line does have a ending point with a closed circle. This means that this is a real point and not a placeholder so the equation x if x is greater than or equal to 2 would work for the top line. The bottom line has an open circle so this mean it is not a real point it is just a placeholder. This line is pointing upward toward the second quadrant with an arrow. The equation -.5x+-.5 if x is less than 1 (not equal to because the circle is open) . One misconception I had was with when two points were at the same coordinate but from different functions and had different end points. For example lets say two graphs have converge on the same point but one graph has a closed circle and the other has a open...
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