### Erin Horst

Produce several (5 to 10) graphs of

on the same axes using different values for d. Does varying d change the shape of the graph? the position?

Let's first begin by exploring the function

We can do this by changing values of d and see what happens to the graph. Let us view a movie where d changes between -5 and 5.

After viewing the movie we can begin to answer the question: does varying d change the shape of the graph? the position? We can conclude from the movie that d shifts the graph of the functions to either the left or right across the x-axis. Why is this? Let's recall that when making adjustments to the identity function y = x, by adding or subtracting values to x, i.e. y = (x - (-d)), y = (x- (d)), these adjustments create a shifting of the graph of the function. We know that if d < 0, then the graph of the function will be shifted to the left and if d > 0, then the graph of the function will be shifted to the right.

Since we know that the d causes the graph to shift horizontally along the x-axis, we can also realize that d will not change the shape of the graph. Let's recall that to make a graph stretch or compress we would need to be multiply either the variable x by some a (y = ax) or f(x) by some a (y = af(x)).

We have concluded through our exploration that when changing the d within the equation

the graph of the function is shifted horizontally along the x-axis.

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