Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value Function
The absolute value function, denoted as |x|, represents the distance of a number x from zero on the number line, regardless of direction. This means that the output is always non-negative. For example, |3| = 3 and |-3| = 3. In the context of the function h(x) = |-(1/2)x|, the absolute value affects the shape of the graph, ensuring it is always above the x-axis.
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Linear Functions
Linear functions are mathematical expressions that create a straight line when graphed. They can be represented in the form y = mx + b, where m is the slope and b is the y-intercept. In the function h(x) = |-(1/2)x|, the linear component is -(1/2)x, which indicates a slope of -1/2, meaning the line descends as it moves from left to right before being reflected upwards by the absolute value.
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Graphing Techniques
Graphing techniques involve plotting points on a coordinate plane to visualize mathematical functions. For the function h(x) = |-(1/2)x|, one would first graph the line y = -(1/2)x, then reflect any portions of the graph that fall below the x-axis to create the final graph of the absolute value function. Understanding how to manipulate and reflect graphs is crucial for accurately representing functions involving absolute values.
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Graphs and Coordinates - Example