Question
Begin by graphing the square root function, f(x)equalsStartRoot x EndRoot. Then, use transformations of this graph to graph the given function.
h left parenthesis x right parenthesis equals negative StartRoot x plus 9 EndRoot
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Part 1
What transformations are needed to graph the function h left parenthesis x right parenthesis equals negative StartRoot x plus 9 EndRoot? Choose the correct answer below.
A.
The graph of StartRoot x EndRoot should be horizontally shifted to the left by 9 units and reflected about the x-axis.
B.
The graph of StartRoot x EndRoot should be horizontally shifted to the right by 9 units and reflected about the y-axis.
C.
The graph of StartRoot x EndRoot should be horizontally shifted to the left by 9 units and reflected about the y-axis.
D.
The graph of StartRoot x EndRoot should be horizontally shifted to the right by 9 units and reflected about the x-axis.
h left parenthesis x right parenthesis equals negative StartRoot x plus 9 EndRoot
Question content area bottom
Part 1
What transformations are needed to graph the function h left parenthesis x right parenthesis equals negative StartRoot x plus 9 EndRoot? Choose the correct answer below.
A.
The graph of StartRoot x EndRoot should be horizontally shifted to the left by 9 units and reflected about the x-axis.
B.
The graph of StartRoot x EndRoot should be horizontally shifted to the right by 9 units and reflected about the y-axis.
C.
The graph of StartRoot x EndRoot should be horizontally shifted to the left by 9 units and reflected about the y-axis.
D.
The graph of StartRoot x EndRoot should be horizontally shifted to the right by 9 units and reflected about the x-axis.
Answers
GPT-4o mini
To analyze the function \( h(x) = -\sqrt{x + 9} \), we need to consider how transformations apply to the basic graph of \( f(x) = \sqrt{x} \).
1. **Inside the square root**: The expression inside the square root, \( x + 9 \), means we will perform a horizontal shift. Since it is \( x + 9 \), this indicates a shift to the **left** by 9 units.
2. **Negative sign outside the square root**: The negative sign in front of the square root indicates a reflection across the **x-axis**.
Putting these two transformations together:
- You shift the graph of \( \sqrt{x} \) left by 9 units,
- Then reflect the resulting graph about the x-axis.
Therefore, the correct option is:
**A. The graph of \( \sqrt{x} \) should be horizontally shifted to the left by 9 units and reflected about the x-axis.**
1. **Inside the square root**: The expression inside the square root, \( x + 9 \), means we will perform a horizontal shift. Since it is \( x + 9 \), this indicates a shift to the **left** by 9 units.
2. **Negative sign outside the square root**: The negative sign in front of the square root indicates a reflection across the **x-axis**.
Putting these two transformations together:
- You shift the graph of \( \sqrt{x} \) left by 9 units,
- Then reflect the resulting graph about the x-axis.
Therefore, the correct option is:
**A. The graph of \( \sqrt{x} \) should be horizontally shifted to the left by 9 units and reflected about the x-axis.**