Chapter 1.3, Problem 83E

(a)

To determine

To calculate: To find the coordinates of a second point on the graph of a function if the given point is on the graph and the function is even

Answer to Problem 83E

Second coordinate is $\left(-x,-y\right)$

Explanation of Solution

  

Given: Point is $\left(x,-y\right)$

Formula Used:

Even Function: If the graph of function has symmetry about y-axis as shown below:

  

For point $\left(x,y\right)$ lying on the graph, $\left(-x,y\right)$ also lies on the graph

Calculation:

Point is given as follows:

  $\left(x,-y\right)$

Since the function is even and point lies on graph.

Thus, coordinates of second point that lies on graph is as follows:

  $\left(-x,-y\right)$

Conclusion:

Hence, second coordinate is $\left(-x,-y\right)$

(b)

To determine

To calculate: To find the coordinates of a second point on the graph of a function if the given point is on the graph and the function is odd

Answer to Problem 83E

Second coordinate is $\left(-x,y\right)$

Explanation of Solution

  

Given: Point is $\left(x,-y\right)$

Formula Used:

Odd Function: If the graph of function has symmetry about origin as shown below:

  

For point $\left(x,y\right)$ lying on the graph, $\left(-x,-y\right)$ also lies on the graph

Calculation:

Point is given as follows:

  $\left(x,-y\right)$

Since the function is odd and point lies on graph.

Thus, coordinates of second point that lies on graph is as follows:

  $\left(-x,y\right)$

Conclusion:

Hence, second coordinate is $\left(-x,y\right)$