Chapter 11.7, Problem 46PPE

To determine

To solve the function $y=\frac{1}{{(x-1)}^2}$ with a dashed line.

Answer to Problem 46PPE

Dashed line x = 2 unit translated by right are vertical asymptote

Explanation of Solution

Given:

Given function

  $y=\frac{1}{{(x-1)}^2}$

Calculation:

In order to solve the equation $y=\frac{1}{{(x-1)}^2}$ ,

  $\begin{array}{l}y=\frac{1}{{(x-1)}^2}\\ $ {(x-1)}^2=0$x=1\\ verticalasymptote\end{array}$

Considering the values of x and y put the values in function

x	$y=\frac{1}{{(x-1)}^2}$	(x, y)
4	$y=\frac{1}{{(x-1)}^2}$  y = 0.11	(4, 0.11)
2	$y=\frac{1}{{(x-1)}^2}$  y = 1	(2, 1)
0	$y=\frac{1}{{(x-1)}^2}$  y = 1	(0, 1)
-2	$y=\frac{1}{{(x-1)}^2}$  y = 0.11	(-2, 0.11)
-4	$y=\frac{1}{{(x-1)}^2}$  y = 0.04	(-4, 0.

  

For a dashed line see denominator of function $x=2$

So the graph in 2^nd quadrant translated by 2 unit right

  $x=2$ are dashed line of vertical asymptote

Thus, the solution is correct.