Question

Rational functions v and w both have a point of discontinuity at x = 7. Which equation could represent function w?
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

Answer 1

Answer:D

Step-by-step explanation:

Edmentum moment

Answer 2

The equation that could represent rational function $w$ is $w(x) = v(x-7) + 7$. (Correct choice: C)

Rational functions become undefined when denominator becomes zero. Let be $v$ and $w$ both rational functions whose point of discontinuity is at $x = 7$, for rational functions a point of discontinuity happens when:

$q(x) = r(x-a)$, $x = a$ (1)

According to this case, we must observe the following relationship, that is, a combination of a parent rational function and a vertical translation:

$w(x) = v(x-a) + k$, $\forall \,k\in \mathbb{R}$ (2)

If we know that $a = 7$ and $k = 7$, then the equation that may represent function $w$ is:

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

Thus, the equation that could represent rational function $w$ is $w(x) = v(x-7) + 7$. (Correct choice: C)

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