Chapter 3, Problem 15SGA

To determine

To find: Whether the graph of $xy=4$ is symmetric with respect to the x-axis, y-axis, the line y = x, the line $y=-x$ or none of these.

Answer to Problem 15SGA

  $y=x\text{ and }y=-x$

Explanation of Solution

Given information: $xy=4$

Calculation:

Replace a, b with a, - b for symmetry with x-axis

  $a\left(-b\right)\ne 4$

Replace a, b with − a, b for symmetry with the y-axis

  $\left(-a\right)b\ne 4$

Replace a, b with b, a for symmetry with the line y = x

  $ba=4$

Replace a, b with − a, - b for symmetry with the line $y=-x$

  $\left(-b\cdot -a\right)=4$

Thus,

  $y=x\text{ and }y=-x$