How does the graph of the transformed function compare to the graph of its parent
function ?
(1 point)
The transformed function has been reflectéd over the -axis, vertically stretched by a factor of 2 , and translated 5
units to the left.
The transformed function has been reflected over the -axis, vertically stretched by a factor of 2 , and translated 5
units to the left.
The transformed function has been reflected over the -axis, vertically stretched by a factor of 2 , and translated 5 .
units to the right.
The transformed function has been reflected over the -axis, vertically stretched by a factor of 2 , and translated 5
units to the right.

Ask by Hodgson Ryan. in the United States

Jan 04,2025

Question

How does the graph of the transformed function compare to the graph of its parent
function ?
(1 point)
The transformed function has been reflectéd over the -axis, vertically stretched by a factor of 2 , and translated 5
units to the left.
The transformed function has been reflected over the -axis, vertically stretched by a factor of 2 , and translated 5
units to the left.
The transformed function has been reflected over the -axis, vertically stretched by a factor of 2 , and translated 5 .
units to the right.
The transformed function has been reflected over the -axis, vertically stretched by a factor of 2 , and translated 5
units to the right.

Ask by Hodgson Ryan. in the United States

Jan 04,2025

UpStudy AI · Accepted Answer

The transformed function $$ g(x) = -2 \log _{2}(x-5) $$ compared to the parent function $$ f(x) = \log _{2} x $$ undergoes the following transformations:

1. **Horizontal Translation**: $$ (x - 5) $$ shifts the graph **5 units to the right**.
2. **Vertical Stretch**: The factor of **2** stretches the graph **vertically by a factor of 2**.
3. **Reflection**: The negative sign **$$-2$$** reflects the graph **over the $$ x $$-axis**.

**Correct Option:**
- The transformed function has been reflected over the $$ x $$-axis, vertically stretched by a factor of 2, and translated 5 units to the right.

**Answer:**
The transformed function has been reflected over the x-axis, vertically stretched by a factor of 2, and translated 5 units to the right.
The transformed function $$ g(x) = -2 \log _{2}(x-5) $$ is reflected over the $$ x $$-axis, stretched vertically by a factor of 2, and shifted 5 units to the right compared to the parent function $$ f(x) = \log _{2} x $$.

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