Chapter 12.5, Problem 31STP

To determine

Identify the function represented by graph.

Answer to Problem 31STP

Inverse variation or rational function.

Explanation of Solution

Given information:

  

Calculation:

The graph represents the function,

  $f\left(x\right)=\frac{k}{x}isahyperbola$ . It has two branches in opposite quadrants.

If $k>0$ , the branches lies in quadrant $IandIII$

If $k<0$ , the branches lies in quadrant $IIandIV$

The graph appears to not cross the axes. In fact, it is true of any inverse variation

The domain and range of inverse variation function are,

  $\begin{array}{l}Domain:x\ne 0\\ Range:y\ne 0\end{array}$

Hence the graph represents the inverse variation or rational function.