Question
Question 2 Let \( f(a)=2^{2} \) be the parent function. Let \( g(x)=2^{9+0} \) be a transformation of the parent function. Describe the change from the parent function. Ots shift up 6 units shift left 6 units shift right 6 units shift down 6 units
Ask by Reese Olson. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The function \( g(x) = 2^{x - 6} \) shifts the parent function \( f(x) = 2^x \) **6 units to the right**.
Solution
It appears there might be a slight misunderstanding or typo in the functions provided. Let's clarify and address the transformation based on typical exponential function transformations.
**Parent Function:**
\[ f(x) = 2^x \]
**Transformed Function:**
\[ g(x) = 2^{x - 6} \]
This transformation can be interpreted as a horizontal shift. Specifically:
- The expression \( x - 6 \) inside the exponent indicates a **shift to the right by 6 units**.
**Explanation:**
- In exponential functions, replacing \( x \) with \( x - h \) results in a horizontal shift to the right by \( h \) units.
- Conversely, \( x + h \) would shift the graph to the left by \( h \) units.
**Therefore, the correct transformation is:**
**Shift right 6 units**
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
The transformation of the parent function \( f(a) = 2^2 \) to \( g(x) = 2^{9 + 0} \) involves raising the exponent from 2 to 9. This indicates a vertical shift upwards in the graph, moving it 7 units up since \( 9 - 2 = 7 \). So, your original function gets a boost, stretching it higher on the y-axis! Think of this transformation as giving \( f(a) \) a little pep talk—it's not just standing there anymore; it’s reaching up towards the sky! The new function becomes steeper and moves higher, which could also reflect in real-world scenarios like exponential growth in populations or finances where growth rates can significantly alter outcomes.
