Question

If the relationship between the manipulated variable and the responding variable is an inverse proportion, what will a line graph of this relationship look like?
A. a straight line
B. a curved line
C. a jagged line
D. none of the above

Answer 1

The correct answer for this question is "B. a curved line." If the relationship between the manipulated variable and the responding variable is an inverse proportion, the line graph of this relationship will look like a a curved line. Inverse of that line will give you a curved line.

Answer 2

For this case we have a function of the form:

$y = \frac{k}{x}$

Where,

y: dependent variable

x: independent variable

k: constant

Since the relationship is inverse, then the graph is a curve. The behavior of the function is:

When the value of x is very close to zero on the right the graph tends to infinity.

When the value of x is a very large number (positive) the graph tends to zero.

When the value of x is very close to zero on the left the graph tends to minus infinity.

When the value of x is a very large number (negative) the graph tends to zero.

Answer:

a line graph of this relationship looks like:

B. a curved line