Chapter 11.7, Problem 32PPE

To determine

Write equations of two rational functions with graphs vertically shifted 3 units.

Answer to Problem 32PPE

  $x=\frac{6}{y},x=\frac{6}{y-3}$

Explanation of Solution

Given:

  

Concept Used:

• Asymptote: if the graph does not cross each other axis. the axis in this graph function as asymptote.
• Vertical asymptote: when the numerator and denominator of a rational function have no common factors other than 1 is to be vertical asymptote.

Calculation:

In order to solve the question

Let rational function

  $\begin{array}{l}x=\frac{6}{y},x=\frac{6}{y-3}\\ y=0,y=3\\ y=3\text{}(horizontalasymptote)\end{array}$

  

  

From the above graph, both the graphs are identical but first graph does not approach each other axis while second graph cross each other vertically with $y=3$

Line translated by 3 units so line $x=3$ are asymptote

Thus, the solution is correct.