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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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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