Sketching fuctions - standard meaning of terms? When sketching the graphs of polynomials, do certain terms always have the same meaning?

For example, in $f(x) = x^n + c$, the intersection with the y-axis is always $c$, no matter how high the degree of the polynomial (because $c$ is a constant of course). But I was wondering whether or not for example $x^1$ or $x^2$ and so forth also always have a certain 'effect' on a function, which would make sketching them easier.
The highest-order term of a polynomial always determines its general behavior very far from the origin. Low-order terms always are good estimates sufficiently close to the origin.
The highest-order term of a polynomial always determines its general behavior very far from the origin. Low-order terms always are good estimates sufficiently close to the origin.