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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.

sradms0
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  • Can you make your question clearer? – Nick Oct 16 '16 at 17:17
  • Are you sure it's not $(1/2)x$ where you wrote $1/2x$. You should also quote the book's words exactly. – Ethan Bolker Oct 16 '16 at 17:18
  • Sorry, yes, I have been getting so frustrated with this that my typing is furious. Here it is: "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. – sradms0 Oct 16 '16 at 17:19

1 Answers1

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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.

This

theideasmith
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