170- Quiz 2

Quiz 2 is here.

Solutions follow.

Problem 1 asks for the graph of , beginning with the graph of

For this, note that the new graph is the result of translating the original graph one unit to the right (on account of being replaced with ) and one unit up (on account of being 1 larger than ).

In the graph (click to enlarge), I have highlighted both axes, and drawn in blue the required curve and in black the graph of , for comparison. Note that the required graph goes through the origin; this corresponds to being in the original graph.

Problem 2 asks to find when , to simplify this as much as possible, and to determine what happens when approaches 0. In other words, we want to find a formula for .

We have , so . It follows that and therefore

Note that this is a constant, and therefore its value does not change as approaches 0, i.e., . This corresponds to the fact that straight lines have the same slope at all points.

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