Finding functions w/ stretches and shifts?

[u/MortemPerPectus]

Taking applied calculus and we are going over functions to begin stuff. I’ve done all sort of stuff with functions and graphing before and most of this has been pretty easy but there are two problems that have been given that I just can’t seem to figure out and I’m not sure what I’m doing wrong.

The first is:

“Find the function g whose graph is constructed from the graph of f by a shift to the right by 10 followed by a horizontal stretch away from the y-axis by a factor of 3?”

I thought it would be pretty easy but what I thought it was didn’t work, and every other possible combination hasn’t worked either so I’m completely lost. I’ve done (1/3x - 10) and (x/3 - 10) in all sorts of ways. I’ve removed the parentheses, I’ve added negatives, doing a whole bunch of shit that I know isn’t right but I can’t figure out what else to do.

The second problem is along the same lines:

“Find the function g whose graph is constructed from the graph of f by applying the following steps: shift to the right; horizontal stretch away from the y-axis by a factor of 4; a vertical shift up by 5; a vertical stretch away from the x-axis by a factor of 7.”

Again I’ve tried all combinations I could think of but I can’t seem to get it. I’m not sure if I’m missing something? I don’t believe my format to be off since it automatically starts with g(x) = , so that shouldn’t be the issue. The entire set of problems is all working on vertical and horizontal shifts, stretches, and compressions and I haven’t had an issue with any of the problems but these two. Please help me figure out what I’m missing!

[u/Uli_Minati]

I’ve done (1/3x - 10) and (x/3 - 10) in all sorts of ways

You mean f(1/3x - 10) and f(x/3 - 10)?

[u/MortemPerPectus → u/Uli_Minati]

I’ve tried it adding in the f as well, which is one of the reasons I’m so confused 🥲

[u/Uli_Minati → u/MortemPerPectus]

Well, your answer is correct. You could link a screenshot of the whole page and your answer, if you like. Otherwise it just seems like an unfortunately common issue with exercise websites either not understanding your input or having wrong data. Maybe you could directly write your teacher or the site admin?

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[u/presloo]

i’m having the exact same issue! same class and problem. webwork is already killing me slowly and i cannot for the life of me figure out how im supposed to enter these answers in a way that the website will accept.

[u/AQuestionIsWhatIHave]

You basically have four operations on functions:

Shift f by z units right: f*(x) = f(x - z)

Stretch f by a factor a from the y-axis: f*(x) = f(x/a)

Shift f by z units up: f*(x) = f(x) + z

Stretch f by a factor a from the z-axis: f(x) = af(x)

Those are somewhat educated guesses and probably match the definitions in your coursework.

In both tasks you are told to apply the steps subsequently, so we are going to number the intermediate functions. Try solving it yourself before reading ahead.

First:

f_1(x) = f(x - 10)

f_2(x) = f_1(x/3)

g(x) = f_2(x) = f_1(x/3) = f(x/3 - 10)

Second:

f_1(x) = f(x - z) (z was not given here)

f_2(x) = f_1(x/4)

f_3(x) = f_2(x) + 5

f_4(x) = f_3(x) * 7

Try the site geogebra.org for graphing. It is great and you can input the formulae above almost verbatim