Precalculus Textbook 8th Edition Section 1.6 Exercise 63 Solution

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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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