Given the Following Information About Limits, Sketch a Graph Which

question 6

Essay

Given the following information about limits, sketch a graph which could be the graph of y = f (x). Label all horizontal and vertical asymptotes. $$\begin{array} { l l } \lim _ { x \rightarrow \infty } f ( x ) = \lim _ { x \rightarrow - \infty } f ( x ) = 1 \quad\quad\quad \lim _ { x \rightarrow - 1 ^ { + } } f ( x ) = \lim _ { x \rightarrow 1 ^ { - } } f ( x ) = - \infty \\\lim _ { x \rightarrow - 1 ^ { - } } f ( x ) = \lim _ { x \rightarrow 1 ^ { + } } f ( x ) = \infty \quad\quad f = ( 0 ) = - 1\end{array}$$

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Definitions:

Primary Consumer

An animal that eats producers (e.g., plants or algae).

Decomposer

Organisms, primarily bacteria and fungi, that break down dead organic material, contributing to nutrient recycling in ecosystems.

Caterpillar

The larval stage of butterflies and moths, which is typically a voracious feeder on leaves before undergoing metamorphosis.

Secondary Consumer

An animal that eats herbivores (primary consumers).