Chapter 11.7, Problem 30PPE

To determine

To solve the function $f(x)=\frac{7}{x},f(x)=\frac{7}{x+12}$ with translation graph

Answer to Problem 30PPE

Translated by $-12$ units left

Explanation of Solution

Given:

Given function

  $f(x)=\frac{7}{x},f(x)=\frac{7}{x+12}$

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 function

  $\begin{array}{l}f(x)=\frac{7}{x},f(x)=\frac{7}{x+12}\\ asweknowthatf(x)=y\\ y=\frac{7}{x},y=\frac{7}{x+12}\\ x=0,x=-12\\ y=7,y=7\end{array}$ ,

X	-25	-20	-15	-10	-5	0	5	10
Y	-0.5	-1	-2	3	1	0.8	0.5	0.2

  

  

Here both the graphs are identical but the second graph is translated by -12 units left.

Here is the first graph is approach both the axis but does not cross each other but the second graph

  $herey=7andx=-12$

Thus, the solution of the given equation is $y=7$ is horizontal asymptote and $x=-12$ is vertical asymptote

Thus, the solution is correct.