Are square root functions a group of functions or a function? (Precalculus)

[User1php]

Are square root functions a group of functions or a function? (Precalculus)

 

[skeeter]

What do you mean by a "group" ?

 

[JeffM]

[MATH]\sqrt{x}[/MATH] is a single function, but you can compose it with other functions to create a family of functions like

[MATH]f(x) = 3\sqrt{|x|} + 2[/MATH]
[MATH]f(x) = - \sqrt{2x^2 + 2}[/MATH]
Does this answer your question?

 

[Dr.Peterson]

Are square root functions a group of functions or a function? (Precalculus)

Have you seen the phrase "square root functions" in your textbook or somewhere? If so, they probably define what they mean by that.

JeffM has a reasonable interpretation of what it can mean, but it's not a general term that has a specific meaning all mathematicians would agree on. Normally, we just talk about "the square root function".

When I search for the phrase (specifically as a plural), it appears to be used typically for basic transformations (shifts, stretches, reflections) of the square root function.

 

[User1php]

[MATH]\sqrt{x}[/MATH] is a single function, but you can compose it with other functions to create a family of functions like

[MATH]f(x) = 3\sqrt{|x|} + 2[/MATH]
[MATH]f(x) = - \sqrt{2x^2 + 2}[/MATH]
Does this answer your question?

Yes, thanks!