How Do Two Graphs Differ?

Suppose that the graph of a function f is known. Explain how the graph of y = 4•f(x) differs from the graph of y = f(4x).


Let me see.

For the graph of y = 4•f(x), we stretch the graph vertically because 4 > 1.

For the graph of y = f(4x), we compress the graph horizontally because 4 > 1.

You say?

 

Yes. "Vertically" with respect for the y-axis and "horizontally" with respect for the x-axis.
I had a teacher that was cruelly particular about this. Would regularly switch the axes on tests to make sure we were paying attention to the orientation of the graphs themselves. It hurt. I never forgot. Is this academic trauma response?

 

Academic trauma response?

 

Yeh. A response ingrained deep into the psyche and originating in an experience from within the world of academia.

 

Let's stay focused on mathematics. I am not interested in deep psychological discussions or philosophy.

 

Vaquita3 was only trying to be friendly and make a joke about their days in college. I was trying to discuss philosophy. Please forgive me, I accept you are not interested in philosophy, or how it merges with mathematics. Good Luck in your studies!

 

I am not offended. At 59, however, I don't have time for jokes and philosophy, well, that's another course.

 

Your explanation is spot on!

When we have y = 4•f(x), the graph is stretched vertically by a factor of 4, since multiplying the function by 4 stretches it vertically.

On the other hand, with y = f(4x), the graph is compressed horizontally by a factor of 1/4. This is because replacing x with 4x inside the function causes it to compress horizontally.

Your understanding highlights the essential differences in how these two transformations affect the graph. Great job!

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