Example Question 8

Example corresponding to question 8 in college algebra 2.

Example 1


Function f has its graph completely in Quadrant $III$. Where will the graph of the inverse function of $f$ be?

  1. $IV$
  2. $II$
  3. $I$
  4. $III$
  5. $I$ and $II$

Solution


  1. According to the 5 possible answers, we are looking for a quadrant.

  2. By definition of the inverse function if $(a,b)$ is a point on the graph of $f$, then the point $(b,a)$ is on the graph of its inverse.

  3. To find in which quadrant is a point located, we need to find the signs of its coordinates. If the graph of is in quadrant $III$, then both coordinates $a$ and $b$ are negative. Hence the point $(b,a)$ on the graph of the inverse also has both coordinates negative and therefore the graph of the inverse is located in quadrant $III$.

    Answer D