## Precalculus Textbook 8th Edition Section 1.6 Exercise 63 Solution

**Question**:

Given a function f, which of the following represents a vertical translation of 2 units upward, followed by a reflection across the y-axis?

**Option A**: y = f(-x) + 2

**Option B**: y = 2 – f(x)

**Option C**: y = f(2 – x)

**Option D**: y = -f(x – 2)

**Option E**: y = f(x) – 2

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**Solution**:

Let a function is y = f(x)

Now, if x is replaced by -x, then the graph of the function f(-x) is a reflection of the graph of f(x) across y-axis.

Now, if 2 is added to f(x), the whole graph of the function f(x) translates vertically of 2 units upward.

Thus, y = f(-x) + 2 represents a vertical translation of 2 units upward, followed by a reflection across the y-axis. (**Option A**)

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