Question

explain why zero cannot be in the domain of an inverse variation.

choose the correct answer below.
a. the graph of an inverse variation function will always be positive.
b. the graph of an inverse variation function will never go through the point (0,0).
c. division by zero is always 0.
d. division by zero is undefined.

Explanation:

An inverse variation is defined by the equation $y = \frac{k}{x}$ where $k$ is a non-zero constant. If $x=0$ (zero in the domain), this would require dividing the constant $k$ by 0, which is a mathematically undefined operation. Option A is incorrect because inverse variation graphs can be negative. Option B is a result of zero not being in the domain, not the reason. Option C is false because division by zero is not 0, it is undefined.

Answer:

D. Division by zero is undefined.