Phillips Jimenez
08/25/2024 · Junior High School
Describe how the graph of the function can be obtained from one of the basic graphs. \( f(x)=5 \sqrt{x}-6 \) Start with the graph of \( h(x)=\sqrt{x} \). Then \( \square \) by a factor of \( \square \). Finally, shift it \( \square \) unit(s). (Type an integer or a simplified fraction.)
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Step-by-step Solution
To obtain the graph of the function \( f(x) = 5 \sqrt{x} - 6 \) from the basic graph \( h(x) = \sqrt{x} \), we can follow these steps:
1. **Vertical Stretch**: The function \( f(x) = 5 \sqrt{x} \) represents a vertical stretch of the graph of \( h(x) = \sqrt{x} \) by a factor of \( 5 \). This means that every point on the graph of \( h(x) \) is multiplied by \( 5 \).
2. **Vertical Shift**: The term \( -6 \) indicates a vertical shift downward by \( 6 \) units. This means that after stretching the graph, we will move it down by \( 6 \) units.
Putting this all together, we can fill in the blanks:
- Start with the graph of \( h(x) = \sqrt{x} \).
- Then **stretch** by a factor of **5**.
- Finally, shift it **6** unit(s) downward.
So the completed statement is:
Start with the graph of \( h(x) = \sqrt{x} \). Then stretch by a factor of \( 5 \). Finally, shift it \( 6 \) unit(s) downward.
Quick Answer
Start with the graph of \( h(x) = \sqrt{x} \). Then stretch by a factor of \( 5 \). Finally, shift it \( 6 \) units downward.
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