Question

select the correct answer.

function \\(f(x) = \frac{1}{x}\\) is shifted 7 units right to \\(w(x)\\). which equation represents \\(w(x)\\)?

\\(w(x) = \frac{1}{x} - 7\\)

\\(w(x) = \frac{1}{x + 7}\\)

\\(w(x) = \frac{1}{x - 7}\\)

\\(w(x) = \frac{1}{x} + 7\\)

Explanation:

Apply horizontal shift transformation rule

$$ w(x) = f(x - c) \quad \text{for a shift of } c \text{ units right} $$

Substitute the given function and shift value

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Answer:

• \(w(x) = \frac{1}{x} - 7\)
• \(w(x) = \frac{1}{x + 7}\)
• \(w(x) = \frac{1}{x - 7}\) (Correct answer)
• \(w(x) = \frac{1}{x} + 7\)