Let’s graph functions of the form
on the same set of axes, where
.
At first observation, we can see that graphs whose coefficients are more positive experience a more drastic vertical stretch. Since each graph experiences a y-intercept at exactly the same point, let’s explore the distinct x-values for which each graph yields a y-value of 1.
Let’s see if we can find a scaling of each a that well help us achieve the desired corresponding x-value.
Now let’s put the coefficient of each entry in the third column in terms of its corresponding x-value in the second column.
