Q2: Explain the effect of replacing x by cx in the equation of a graph
A2:
One way to understand this is to note that to graph what we plot at is the y-value of . That is, to find the y-value on our new graph we look on the old graph at the point c times as far from the y-axis (i.e. further away if and closer in if ). But if we reach out to find our values, that means that we will pull them in when we plot them (and vice versa). Thinking “Reach out to pull in” (and Reach in to pull out”) may help you to remember the resulting effect on the graph.
The apparent difference between x and y disappears if we note that is the same as . So taking c times the formula for y is the same as replacing y in the equation, not by cy, but rather by .