Temperature readings T (in ^∘ F ) were recorded every 2 hours from midnight to noon in Atlanta,

step 1 We have been given that small t is the time in hours which is measured from midnight and t is th

Temperature readings T (in ^∘ F ) were recorded every 2...

Temperature readings $T$ (in $^{\circ} \mathrm{F}$ ) were recorded every 2 hours from midnight to noon in Atlanta, Georgia, on March $18,2014 .$ The time $t$ was measured in hours from midnight. Sketch a rough graph of $T$ as a function of $t.$ $$\begin{array}{|c|c|c|c|c|c|c|c|} \hline t & 0 & 2 & 4 & 6 & 8 & 10 & 12 \\ \hline T & 58 & 57 & 53 & 50 & 51 & 57 & 61 \\ \hline \end{array}$$

Temperature readings $T$ (in $^{\circ} \mathrm{F}$ ) were recorded every 2 hours from midnight to noon in Atlanta, Georgia, on March $18,2014 .$ The time $t$ was measured in hours from midnight. Sketch a rough graph of $T$ as a function of $t.$
$$\begin{array}{|c|c|c|c|c|c|c|c|}
\hline t & 0 & 2 & 4 & 6 & 8 & 10 & 12 \\
\hline T & 58 & 57 & 53 & 50 & 51 & 57 & 61 \\
\hline
\end{array}$$

Key Concepts

Graphing a Function

Graphing a function involves plotting a set of ordered pairs on a coordinate plane where each input value corresponds to an output value. This process is fundamental in understanding how one variable (like time) affects another variable (like temperature) and allows one to visualize the relationship between them.

Coordinate System

A coordinate system is used to represent data visually, with a horizontal axis (typically representing the independent variable) and a vertical axis (usually for the dependent variable). Proper labeling and scaling of these axes are essential for accurately interpreting the graph.

Discrete Data Plotting

Discrete data consists of distinct, separate points as opposed to a continuous function. When temperature readings are taken at specific time intervals, each recorded pair is plotted individually, highlighting the data points without implying that the function is continuously defined between them.

Data Visualization

Data visualization encompasses techniques for representing numerical data graphically to reveal patterns, trends, and relationships. Sketching a graph from given data allows one to quickly assess variations over time and facilitates a deeper understanding of the underlying information.

Time Series Analysis

Time series analysis involves examining data points collected or recorded at successive points in time. In plotting temperature as a function of time, one can observe fluctuations, trends, and patterns that provide insights into how the temperature changes throughout the day.

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