Math Problem

[f1123]

Hi, I need help with these math exercises how should I proceed?

Link image:
https://ibb.co/qd6cFSx

[ToraToraTora]

proceed from first principles employing all your mathematical ability.

[bobbinwales]

Are them questions in Italian?? Your better off putting the questions in English as its a UK site. I cant speak no italian but I think the questions mentions maximum and minimum and intervals

[aelmpvw]

looked like double dutch to me . . .

[TherefinedByron]

Hmmm... Looked like French and Latin to me.

[bobbinwales]

observe the following graphs and deduce the following information: domain, intersections, with the sign axes limits to the extremes of the domain and asymptotes, maximums and minimums, monitonic intervals, inflected convexity intervals


Or summat like that

[Buenchico]

Start with the easy stuff. The domain of a function, f(x), is the set of values of x for which f(x) exists.

In 1(a) for example, there appear to be limits to the function at x = -1 and x = 1.5. (e.g. both f(-3) and f(3) are undefined). Therefore the domain of f(x) is {x: x ∈ R, -1 ≤ x ≤ 1.5}.

In 1(b), there appear to be no limits or discontinuities, so the domain of f(x) is simply {x ∈ R}.

I'll leave you to do 1(c) but point out that there are discontinuities, for which f(x) is undefined, at x = -2 and x = 1.

The sign of each function is dead easy. If the graph lies above the y=0, the sign is positive. If it's below, it's negative. You simply need to express that in a mathematical format.

You're next asked for the values of x where the function intersects the axes. That's simply a matter of looking at the graphs to find the relevant points.

From then on, you're on your own but I will point out that the asymptotes are defined on the graphs for you. (There are no asymptotes in 1(a), one in 1(b) and three in 1(c)).

[Buenchico]

Pedantic typo correction:
The set at the end of my third paragraph, above, should of course be {x: x ∈ R}.