I am reviewing some lessons in my textbook for school.
In this example:
y = f(x)
Graph: h(x) = f(1/2x)
For h(x), the book says that 1/2x is dividing each x coordinate by 1/2, but when I look at this, I think that you would multiply each x coordinate by 1/2. What am I not getting?
From the book: "Graph h(x) = f(1/2(x)). Horizontally stretch the graph of y = f(x). Divide each x-coordinate by 1/2, which is the same as multiplying by 2."
Thanks for your help.
We have a graph plotting $f(x)$ for all $x$. However, at any $x$, h(x) will plot $f(\frac{x}{2})$.
Now consider what this means. If we take the value of $h(x)$ at $x=a$, we will only get the same value on $f(x)$ at $x=2a$. This means the graph of $h(x)$ stretches $f(x)$ by a factor of 2, which you can see in the graph.