Here are the essential concepts you must grasp in order to answer the question correctly.
Exponential Functions
Exponential functions are mathematical expressions in the form f(x) = a^x, where 'a' is a positive constant. In the given function, f(x) = 2^(-|x|), the base is 2, and the exponent is the negative absolute value of x. This results in a function that decreases as x moves away from zero, reflecting the properties of exponential decay.
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Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x| and is always non-negative. In the function f(x) = 2^(-|x|), the absolute value affects the exponent, ensuring that the output remains positive for all real values of x, which is crucial for graphing the function.
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Graphing Techniques
Graphing techniques involve plotting points on a coordinate plane to visualize the behavior of a function. For f(x) = 2^(-|x|), one would calculate values for various x inputs, noting that the graph is symmetric about the y-axis due to the absolute value. Understanding how to interpret and sketch the graph is essential for analyzing the function's characteristics, such as its intercepts and asymptotic behavior.
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