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### Which function is shown in the graph below?
A) y=(1 / 2)^x+ 3 - 1
B) y=(1 / 2)^x- 3 + 1
C) y=(1 / 2)^x- 1 + 3
D) y=(1 / 2)^x+ 1 - 3
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Answer
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Step 1:Let's solve this step by step by analyzing the graph and comparing it with the given function options.
Step 2:: Identify the key characteristics of the graph
- The graph is an exponential function with base $$rac{1}{2}
- The graph appears to have a horizontal asymptote - The graph shifts vertically and horizontally from the standard exponential function
Step 3:: Analyze the vertical shift
- The graph appears to be shifted up by 3 units - This suggests the function will have a "+ 3" term
Step 4:: Analyze the horizontal shift
- The graph looks like it's shifted left by 1 unit - This suggests the function will have a "- 1" inside the exponent
Step 5:: Verify the base of the exponential function
- The base is clearly $$rac{1}{2}$$, which means the function is of the form $$y = \left(rac{1}{2}\right)^{x-1} + 3
Step 6:: Compare with given options
- This matches option C: $$y = \left(rac{1}{2}\right)^{x-1} + 3
Final Answer
C) y = \left(rac{1}{2}\right)^{x- 1} + 3
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