Questions: How does the graph of f(x) = 1/2(3)^(x+2) - 1 relate to its parent function? A. The parent function has been stretched. B. The parent function has been translated to the left. C. The parent function has been compressed. D. The parent function has been translated down.

How does the graph of f(x) = 1/2(3)^(x+2) - 1 relate to its parent function? A. The parent function has been stretched. B. The parent function has been translated to the left. C. The parent function has been compressed. D. The parent function has been translated down.
Transcript text: 5:30 $\cdot$II LTE 37 Algebra II Sem 2 1 3.11.3 Quiz: Comparing and Analyzing Function Types Question 7 of 10 How does the graph of $f(x)=\frac{1}{2}(3)^{x+2}-1$ relate to its parent function? A. The parent function has been stretched. B. The parent function has been translated to the left. C. The parent function has been compressed. D. The parent function has been translated down. SUBMIT course.apexlearning.com
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Solution

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Solution Steps

Step 1: Identify the Parent Function

The parent function is $g(x)$. Before any transformations, it serves as the base for our analysis.

Step 2: Determine Transformations

^Vertical Transformations:^ The function is vertically compressed by a factor of 0.5.

^Horizontal Transformations:^ There is no horizontal stretch or compression.

^Translations:^ The function is translated 2 units to the left. The function is translated 1 units down.

Final Answer:

The transformed function $f(x) = 0.5 \cdot g(1(x + 2)) - 1$ undergoes the following transformations: The function is vertically compressed by a factor of 0.5. There is no horizontal stretch or compression. The function is translated 2 units to the left. The function is translated 1 units down.

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