QQuestionMathematics
QuestionMathematics
Which graph represents an exponential function?
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Answer
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Step 1:I'll solve this step by step, focusing on identifying the characteristics of an exponential function.
Step 2:: Recall the characteristics of an exponential function
An exponential function has the general form $$f(x) = a \cdot b^{x}$$, where:
- The graph curves upward or downward - The curve never crosses the x-axis - The y-intercept is always above the x-axis - The graph shows rapid growth or decay
Step 3:: Examine the given graphs
Looking at the graphs, I'll analyze their key characteristics: - Graph A: Shows a curved line that increases rapidly - Graph B: Shows a straight line with constant slope - Graph C: Shows a curved line that decreases rapidly - Graph D: Shows a curved line that increases slowly
Step 4:: Identify the exponential function
- It satisfies the key characteristics of $$f(x) = a \cdot b^{x}
The graph that represents an exponential function is Graph A, because: - It shows rapid, non-linear growth - The curve becomes steeper as x increases
Final Answer
Graph A represents an exponential function.
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