 This is the write-up for Assingnment 2, problem # 7 and #8.

By Doug Westmoreland

This write-up is an exploration of the curves and using Graphing Calculator 2.7.1.

Let's first take a look at how the "a" value in effects the graph. The following are graphs with the "a" value of .1, .5, 1, 2, 5, 10.

a=.1 purple graph : a=.5 red graph : a=1 blue graph : a=2 green graph : a=5 lt.blue graph : a=10 yellow graph We can see from these examples that the "a" value is definitely either narrowing or expanding the graph depending upon the value of a. As the value of "a" gets larger the graph gets narrower. As the value of "a" decreases to zero the graph expands toward the x-axis.

Question: What do you think negative values of "a" will do to the graph? Click here for the answer.

Now let's take a look at how the value of "d" effects the graph of . The following are graphs with the "d" value of -10, -5, -3, -2, -1, 0, 2, 3, 5, 10.

a=-10 (left red) , a=-5 (left purple) , a=-3 (left blue) , a=-2 green , a=-1 lt.blue , a=0 yellow , a=2 black

a=3 (right purple) , a=5 (right blue) , a=10 (right blue) We can see the the "d" value effects the graph of in the graphs above by shifting the graph of either right or left depending upon the value of "d." Click here for a better presentation of the translation of the graph.

SUMMARY

The value of "a" in dialates the graph. If |a| is greater than 1, then the graph will get narrower toward the y-axis. If |a| is between 0 and 1, then the graph will expand toward the x-axis.

The value of "d" in translates the graph of . If "d" is a positive value, the graph will shift to the right "d" units. If the "d" value is negative, then the graph will shift to the left |d| units.

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