Question

select the correct answer.

rational functions \\(v\\) and \\(w\\) both have a point of discontinuity at \\(x = 7\\). which equation could represent function \\(w\\)?

\\(w(x) = v(x - 7)\\)
\\(w(x) = v(x + 7)\\)
\\(w(x) = v(x - 7) + 7\\)
\\(w(x) = v(x) + 7\\)

Explanation:

Identify the condition for discontinuity of the transformed function

$$ \text{Let } D_v \text{ be the set of points of discontinuity of } v(x). \text{ Given } 7 \in D_v. $$

$$ \text{Let } D_w \text{ be the set of points of discontinuity of } w(x). \text{ We require } 7 \in D_w. $$

Analyze the effect of transformations on the point of discontinuity

$$
LATEXBLOCK0
$$

Select the matching equation

$$ w(x) = v(x) + 7 $$

Answer:

• (A) \(w(x) = v(x - 7)\)
• (B) \(w(x) = v(x + 7)\)
• (C) \(w(x) = v(x - 7) + 7\)
• (D) \(w(x) = v(x) + 7\) (Correct answer)