If limx →-∞ f(x)=∞, limx →∞ f(x)=3, and limx →1^+ f(x)=∞, what can you say about any horizontal

step 1 So here, if the limit as X approaches negative infinity from, just in general, is infinity. And

If limx →-∞ f(x)=∞, limx →∞ f(x)=3, and limx →1^+ f(x)=∞,...

If $\lim _{x \rightarrow-\infty} f(x)=\infty, \lim _{x \rightarrow \infty} f(x)=3$, and $\lim _{x \rightarrow 1^{+}} f(x)=\infty$, what
can you say about any horizontal and vertical asymptotes of $f$ ?

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Key Concepts

Horizontal Asymptote

A horizontal asymptote is a line that the graph of a function approaches as the independent variable (usually x) tends to positive or negative infinity. If the limit of a function as x approaches infinity or negative infinity equals a constant, then the line y = [that constant] is the horizontal asymptote, describing the end behavior of the function.

Vertical Asymptote

A vertical asymptote is a line x = a where the function grows without bound (either to infinity or negative infinity) as x approaches a from the left or right. This often occurs at points where the function is undefined due to discontinuities, such as division by zero or other singularities.

Limit

The concept of a limit involves determining the value that a function approaches as the input approaches some specified point. Limits are essential in analyzing the behavior of functions near points of discontinuity and at the extremities of their domains, and they are the basis for identifying both vertical and horizontal asymptotes.

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