Use a graphing utility to sketch a graph of each function....

Use a graphing utility to sketch a graph of each function. Use trial and error to find a graphing window so that your graph represents the local and global behavior of the function. Include the $x$ and $y$ ranges of your window in your answer.
$$
f(x)=x^{2}-0.1
$$

Key Concepts

Graphing Utility

A graphing utility is a software tool that allows you to visualize functions by automatically plotting their graphs based on the input equation. It is an essential resource for exploring and understanding the behavior of functions, as it can display detailed characteristics of the graph such as intercepts, turning points, and asymptotic behavior.

Graphing Window Selection

Selecting an appropriate graphing window involves choosing the ranges for the x-axis and y-axis that best display the significant features of the function, both locally and globally. This process often involves trial and error in order to ensure that important details, such as extrema and intercepts, are visible and that the overall shape of the graph is accurately represented.

Quadratic Functions

A quadratic function, typically expressed in the form ax² + bx + c, represents a parabola when graphed. The key features of a quadratic include its vertex (which can be a minimum or maximum), axis of symmetry, and intercepts. Understanding these features is critical for sketching the graph and interpreting the behavior of the function.

Local and Global Behavior

Local behavior refers to the characteristics of the function in a specific, small interval (such as around a vertex or near a point of inflection), whereas global behavior describes the overall trend of the function across its entire domain. Capturing both aspects is important when setting a graphing window so that the graph reflects all critical traits of the function.

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