Write up 1: #6

# Logarithmic Functions Changing a,b, and c

by

Elizabeth Mundell

By examining the graph of

you can see how changing the values of a, b, and c effect the appearance of the graph.

By first looking at a we can see that the negative a values create a graph that is below the horizontal line. As the negative a values move farther in the negative direction, it looks like the graph moves leftward.

We can see that the positive a values create a graph that is above the horizontal line. As these a values increase, the graph looks like it moves more leftward. The a value of these graphs is present where they intersect the vertical axis. So by changing a you are changing where the graph will intersect the y axis. So if a = 1, the graph will have the point (0,1). This is only the case if b=1 and c=0 though.

Next we can look at different values of b.

We can see that by only changing b that the graph moves towards or away from the vertical axis. Each graph passes through (0,1). Each graph approaches y = 0. For b = 1 the graph approaches y = 0 more slowly than for b = 3. For b = -1 the graph approaches y=0 more slowly than for b = -3.

Finally, we can examine the changing c values

If we start by looking at the green graph where c=1, we can see that the line goes through (0,2). If we look at c=3, we can see that the line goes through point (0,4). By looking at different graphs I was able to see that the c shifts the graph up or down depending on its value. C creates this point on the line of the graph: (0, c+1). C is responsible for a vertical shift in these graphs.