Stewart Olson
03/09/2023 · High School
Describe how the graph of the following function can be obtained from one of the basic graphs. \( g(x)=|5 x| \) To obtain the graph of \( g(x)=|5 x| \), start with the graph of \( y=\square \) by dividing each \( \square \) it \( \square \) by
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To obtain the graph of the function \( g(x) = |5x| \), we can start with the graph of the basic function \( y = |x| \).
1. **Start with the basic graph**: The graph of \( y = |x| \) is a V-shaped graph that opens upwards, with its vertex at the origin (0,0).
2. **Apply a horizontal scaling**: The function \( g(x) = |5x| \) involves a horizontal scaling of the basic graph. Specifically, we can express this as:
- To obtain the graph of \( g(x) = |5x| \), start with the graph of \( y = |x| \) and apply a horizontal compression by a factor of \( \frac{1}{5} \).
3. **Resulting transformation**: This means that for every point \( (x, |x|) \) on the graph of \( y = |x| \), the corresponding point on the graph of \( g(x) = |5x| \) will be \( \left(\frac{x}{5}, |x|\right) \). This compression makes the V-shape of the graph narrower.
In summary, to obtain the graph of \( g(x) = |5x| \), start with the graph of \( y = |x| \) by dividing each \( x \) value by \( \frac{1}{5} \) (or equivalently, compressing horizontally by a factor of \( \frac{1}{5} \)).
Quick Answer
To obtain the graph of \( g(x) = |5x| \), start with the graph of \( y = |x| \) and apply a horizontal compression by a factor of \( \frac{1}{5} \).
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