Nonlinear function to linear function conversion (as part of linear regression)

[Agent Smith]

How do I change a nonlinear functiom to a linear function?

I'm given [imath]y = x^2[/imath] (parabola/quadratic) and asked to convert it into a linear function.
Something to do with [imath]x^2[/imath], but when I try to graph this (on desmos), I still get a parabola.
[imath]f(x) = x^2[/imath] (parabola)
[imath]g(x) = 3f(x) = 3x^2[/imath] (which I expected to be linear, because it looks like [imath]g(z) = 3z[/imath]), is not)

Gracias

 

[Agent Smith]

A problem in the practice section:
[imath]y = x^2[/imath] and [imath]y = 3x^2[/imath]. The former is a quadratic and the latter is, they say, linear. However, when I plot these two, I get both as parabolas.

 

[Agent Smith]

 

[Dr.Peterson]

Please show exactly what "they" say, in context, including the entire example. You can't change a non-linear function to a linear function, since it isn't. But maybe some particular sort of transformation is allowed, such as a log? We can't know without context.

 

[Agent Smith]

@Dr.Peterson


And yes they do with exponential functions as well (with logarithms).

 

[Dr.Peterson]

I don't see anything said there, just two ambivalent pictures. Please show the whole context, including whatever is actually said.

 

[Agent Smith]

@Dr.Peterson , it's difficult to keep taking screenshots and uploading them.

The gist of the idea seems to be that

1. If the graph for function f vs. x² is a straightline, f is a quadratic: f = mx² + b

2. If the graph for log f and x is a straight line, f is an exponential function: f = [imath]n^x[/imath]

3. If the graph for f and x is a straight line, f is a linear function: y = mx + b

So possibly, if I have f = mx² + b (a quadratic) I can turn it into a linear function. I tried this with f(x) = 3x² + 0 = 3x², but desmos plots it as a parabola/quadratic, not a straight line.


From my notes

 

[BeansNRice]

if I'm understanding this, which it's a fair bet I'm not, OP intends something like this

[imath]f(x) \text{ is non-linear, however } \exists g(x) \ni f(g(x)) \text{ is linear.}[/imath]

My reaction is ... ok so?

 

[Agent Smith]

@BeansNRice I believe you nailed it. Can we do that (convert nonlinear to linear) in desmos. I tried with y = mx² + b: y = 3x² + 2 is not linear, it's still a parabola.

 

[Agent Smith]

I tried many things on desmos but to no avail.

 

[Dr.Peterson]

The gist of the idea seems to be that

1. If the graph for function f vs. x² is a straightline, f is a quadratic: f = mx² + b

2. If the graph for log f and x is a straight line, f is an exponential function: f = nxn^xnx

3. If the graph for f and x is a straight line, f is a linear function: y = mx + b

So there are no actual WORDS you can copy so people can see what someone is supposedly SAYING? And no link you can give for your source?

How do I change a nonlinear functiom to a linear function?

I'm given [imath]y = x^2[/imath] (parabola/quadratic) and asked to convert it into a linear function.
Something to do with [imath]x^2[/imath], but when I try to graph this (on desmos), I still get a parabola.

Show us the actual problem as you see it.

A problem in the practice section:
[imath]y = x^2[/imath] and [imath]y = 3x^2[/imath]. The former is a quadratic and the latter is, they say, linear. However, when I plot these two, I get both as parabolas.

Show us the actual wording of the problem, in context.

If you can't give specific context, we can't be sure we're suggesting the right answers.