How Do Two Graphs Differ?

[harpazo]

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?

 

[Vaquita3]

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?

 

[harpazo]

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?

 

[Vaquita3]

Academic trauma response?

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

 

[harpazo]

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.

 

[conway]

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!

 

[harpazo]

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.

 

[RobertSmart]

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!

And sure, if you need further assistance with math assignments or any other academic help, you might find mathassignmenthelp.com useful. They offer support for various mathematical topics and could be a valuable resource for your assignments. You can also contact them by dialing +1 (315) 557-6473.

 

[harpazo]

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 strictly interested in mathematics.

 

[harpazo]

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!

And sure, if you need further assistance with math assignments or any other academic help, you might find mathassignmenthelp.com useful. They offer support for various mathematical topics and could be a valuable resource for your assignments. You can also contact them by dialing +1 (315) 557-6473.

I am interested in discussing math here. Look for my questions.