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Describe verbally the transformations that can be used to obtain the graph of g from the graph of f
This quiz: 100 point(s) possible
This question: 10 point(s) possible
Ask by Ingram Reid. in the United States
Jan 03,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
To get the graph of
Solution
To obtain the graph of
-
Horizontal Shift (Right by 6 Units):
- The expression
inside the exponent indicates a horizontal shift. - Effect: Move the entire graph of
6 units to the right. This means that every point on will move to on .
- The expression
-
Vertical Scaling (Optional in This Case):
- If there were a coefficient multiplying the exponential function (e.g.,
), it would indicate a vertical stretch or compression. - In this specific function
, there is no such coefficient besides 1, so no vertical scaling is needed.
- If there were a coefficient multiplying the exponential function (e.g.,
Summary of Transformations:
- Shift the graph of
6 units to the right to obtain .
This transformation maintains the shape of the exponential function while repositioning it along the horizontal axis.
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Simplify this solution Extra Insights
To transform the graph of
In practical terms, to sketch
