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The graph of is shown in the xy-plane. Which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?
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Q. The graph of is shown in the xy-plane. Which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?
- Identify Graph Characteristic: The equation given is . We need to identify which characteristic of the graph is represented by a constant or coefficient in the equation.
- Vertical Stretch and Reflection: The coefficient ＂＂ in the equation affects the vertical stretch and reflection of the graph. Since it is negative, it indicates that the graph is reflected across the -axis. The ＂＂ indicates the vertical stretch, meaning the graph is stretched by a factor of from the basic graph of .
- Exponential Function Base: The base ＂＂ in the exponent indicates that the function is an exponential function. The graph of an exponential function with a base greater than will always show exponential growth if the coefficient in front of the base is positive, or exponential decay if it is negative (as in this case).
- Constant Term in Exponential Function: The constant term in an exponential function like would typically be added or subtracted at the end of the equation, such as or , where would affect the vertical translation of the graph. However, there is no such constant term in the given equation.
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