Chapter 11.7, Problem 43PPE

To determine

Determine similarities and differences in the graph $y=\frac{3}{x+2}andy=\frac{-3}{x+2}$

Answer to Problem 43PPE

  $x=-2$ and similarities and differences are given below the graph

Explanation of Solution

Given:

Given equation

  $y=\frac{3}{x+2}andy=\frac{-3}{x+2}$

Calculation:

In order to solve the equation $y=\frac{3}{x+2}andy=\frac{-3}{x+2}$

  $y=\frac{3}{x+2}$   $y=\frac{-3}{x+2}$

x		(x, y)
5	$y=\frac{-3}{x+2}$  y = -0.42	(5, -0.42)
3	$y=\frac{-3}{x+2}$  y = -0.6	(3, -0.6)
1	$y=\frac{-3}{x+2}$  y = -1	(1, -1)
0	$y=\frac{-3}{x+2}$  y = -1.5	(0, -1.5)
-1	$y=\frac{-3}{x+2}$  y = -3	(-1, -3)
-3	$y=\frac{-3}{x+2}$  y = 3	(-3, 3)
-5	$y=\frac{-3}{x+2}$  y = 1	(-5, 1)

x	$y=\frac{3}{x+2}$	(x, y)
5	$y=\frac{3}{x+2}$  y = 0.42	(5, 0.42)
3	$y=\frac{3}{x+2}$  y = 0.6	(3, 0.6)
1	$y=\frac{3}{x+2}$  y = 1	(1, 1)
0	$y=\frac{3}{x+2}$  y = 1.5	(0, 1.5)
-1	$y=\frac{3}{x+2}$  y = 3	(-1, 3)
-3	$y=\frac{3}{x+2}$  y = -3	(-3, -3)
-5	$y=\frac{3}{x+2}$  y = -1	(-5, -1)

  

Here above the graph of both the equations

Similarities:

• Both the graphs are translated by 2 units left
• In both the graphs, line $x=-2$ are vertical asymptote
• In both the graphs excluded value is same i.e. -2

Differences:

• The numerator value of function is 3 and -3
• In first, graph plotted on 1^st and 3^rd quadrant but in second, graph plotted on 2^nd and 4^th quadrant.

  $\begin{array}{l}asx+2=0\\ x=-2\\ which\text{}isaexcludedvalue\end{array}$

Thus, the solution is correct.