function and graph help: composing function w/ itself from its graph

sara343 said:
Not really sure how to go about solving this
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Hello. At this point, it's a bit hard to know what kind of help you need. With respect to students, this is a tutoring web site. In general, we help students by answering specific questions they may have about the process, by checking their work in progress, and by offering corrections, suggestions and sometimes links to online lessons or videos.

Please take a moment to read the complete forum guidelines. (There's also a summary here.)

Please show us anything that you've tried (even if you think it's wrong). It really helps the volunteer tutors, if you also identify any specific concept, notation, steps or parts of an exercise that you find confusing or unfamiliar.

Having said that, I can offer the following, as a start. Although the instructions ask you to use the graph of f(x) to answer the question (i.e., use a graphical method), I would suggest that you work out the composition using paper and pencil. If you don't yet have enough experience with the attributes of compositions of linear functions, the paper-and-pencil approach is the way to go.

f(x) is clearly a linear function. You can write its definition (in slope-intercept form) by inspection, because both its slope and y-intercept are clear, from the graph.

Show us what you get.

Welcome to the boards. :cool:

PS: I deleted your duplicate thread on the calculus board. If you're not sure which board to use going forward, guess and post only once. We can move your thread, if needed. Thank you!
 
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mmm4444bot said:
Hello. At this point, it's a bit hard to know what kind of help you need. With respect to students, this is a tutoring web site. In general, we help students by answering specific questions they may have about the process, by checking their work in progress, and by offering corrections, suggestions and sometimes links to online lessons or videos.

Please take a moment to read the complete forum guidelines. (There's also a summary here.)

Please show us anything that you've tried (even if you think it's wrong). It really helps the volunteer tutors, if you also identify any specific concept, notation, steps or parts of an exercise that you find confusing or unfamiliar.

Having said that, I can offer the following, as a start. Although the instructions as you to use the graph of f(x) to answer the question (i.e., use a graphical method), I would suggest that you work out the composition using paper and pencil. If you don't yet have enough experience with the attributes of compositions of linear functions, the paper-and-pencil approach is the way to go.

f(x) is clearly a linear function. You can write it's definition (in slope-intercept form) by inspection, as both its slope and y-intercept are clear, from the graph. Then compose function f with itself, on paper, using its definition.

If you get stuck, please show us how far you got and explain why you're stuck.

Welcome to the boards. :cool:

PS: I deleted your duplicate thread on the calculus board. If you're not sure which board to use going forward, guess and post only once. We can move your thread, if needed.
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Thanks I wasnt looking for the answers but I really dont know where to begin solving this.

I know that y=mx+b and by the two points given the slope is 1
or b = -1

F(x)= mx +b

I believe that the answers cant be "B" or "C" because those graphs show a parabola and the graph in the problem is a linear function.

So it can only be "A" or "D'

I think its D because that's the only graph where the x coordinates are the same as the points in the graph. but further then that I am not really sure where to start with solving this.
 
Wow. That's a lot of duplicating posting. I have removed those five posts.

I'll try again. Please read the forum guidelines, using the link that I provided. I would like you to read them, before posting again.

You also need to read this announcement.

I asked you to show your work. Do you know how to write the equation of a line?

You posted the correct slope and y-intercept of f(x).

What, then, is the equation for that line? y = ?

Or, if your issue is that you don't know what a composite function is, or how to determine it, then we'll get you some examples. Please let us know.

Thank you! :cool:
 
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I dont have any work because I dont know where to start.
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I told you where to start. :cool: Write the equation of the line shown in the graph of f(x) in slope intercept form, using the numbers for the slope and y-intercept. Show us what you get.

y = ?

… I think the Y intercept is (1,0)
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Please check your typing there. That's not what you posted earlier, for the y-intercept. Also, I'm thinking that you wrote the coordinates in the wrong order. All y-intercepts are in the form (0,?).

Are you familiar with the concept of composition functions? Have you done any before?

I'm looking for some online lessons/videos which specifically show a linear function composed with itself.
 
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Here are some links to a written lesson (mathisfun) and a video (khanacademy) covering the general concept of composing two given functions to arrive at a composite function.

https://www.mathsisfun.com/sets/functions-composition.html

https://www.khanacademy.org/math/al...s/function-composition/v/function-composition


Here is a video of composing one linear function with another (it begins with a short review of the concept of a function, in terms of an input and output):

https://www.youtube.com/watch?v=iOnxgRZfXms&list=PL0G-Nd0V5ZMohmHUdgd-j7lqnoWRGvI_U

I'm not certain, but I think that once this youtube video completes, it then continues through 19 more example videos.



Here is a written example of composing two linear functions (scroll down to example iv).

http://jwilson.coe.uga.edu/emt668/EMAT6680.2003.Su/Daniel/6680/#1/#1-webpage.html



Please study some lessons, work through the given examples on paper (step by step).

Once you think you understand the concept of composite functions (i.e., using the output of one linear function as the input to another linear function), then please try your exercise again.

Please show your work, if you would like more guidance. Thanks! :cool:
 
mmm4444bot said:
I told you where to start. Write the equation of the line shown in the graph of f(x). Show us what you get.


Check your typing here. This is not what you posted earlier, for the y-intercept.

Are you familiar with the concept of composition functions? Have you done any before?

I'm looking for some online lessons/videos which specifically show a linear function composed with itself. :cool:
Click to expand...


Thanks
 
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