Questions: identify the transformations 7. f(x) = 1/2x-2-4

Transcript text: identify the transformations 7. \[ f(x)=\frac{1}{2}|x-2|-4 \]

Solution

Solution Steps

Step 1: Identify the Parent Function

The parent function for this equation is \( f(x) = |x| \), which is the absolute value function.

Step 2: Horizontal Shift

The term \( (x - 2) \) inside the absolute value indicates a horizontal shift. Specifically, the graph is shifted 2 units to the right.

Step 3: Vertical Compression

The coefficient \( \frac{1}{2} \) in front of the absolute value indicates a vertical compression. The graph is compressed vertically by a factor of \( \frac{1}{2} \).

Step 4: Vertical Shift

The term \( -4 \) at the end of the function indicates a vertical shift. The graph is shifted 4 units downward.

Final Answer

The transformations are: 2 units right, vertical compression by a factor of \( \frac{1}{2} \), and 4 units down.

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