Chapter 7.5, Problem 37WE

(a)

To determine

Make a table of values and draw the graph for the relation $x=-y^2$ for integral values of y from -3 to 3.

Explanation of Solution

Calculation:

  $x=-y^2$

Make a table:

y	$x=-y^2$
-3	-9
-2	-4
-1	-1
0	0
1	-1
2	-4
3	-9

Now , plot the above coordinates and join them to get the graph of relation $x=-y^2$:

  

(b)

To determine

Make a table of values and draw the graph for the relation $x=y^2+2$ for integral values of y from -3 to 3.

Explanation of Solution

Calculation:

  $x=y^2+2$

Make a table:

y	$x=y^2+2$
-3	11
-2	6
-1	3
0	2
1	3
2	6
3	11

Now , plot the above coordinates and join them to get the graph of relation $x=y^2+2$:

  

(c)

To determine

Make a table of values and draw the graph for the relation $x={(y+1)}^2$ for integral values of y from -4 to 2.

Explanation of Solution

Calculation:

  $x={(y+1)}^2$

Make a table:

y	$x={(y+1)}^2$
-4	9
-3	4
-2	1
-1	0
0	1
1	4
2	9

Now , plot the above coordinates and join them to get the graph of relation $x={(y+1)}^2$:

  

(d)

To determine

Make a table of values and draw the graph for the relation $x={(y+1)}^2+2$ for integral values of y from -4 to 2.

Explanation of Solution

Calculation:

  $x={(y+1)}^2+2$

Make a table:

y	$x={(y+1)}^2+2$
-4	11
-3	6
-2	3
-1	2
0	3
1	6
2	11

Now , plot the above coordinates and join them to get the graph of relation $x={(y+1)}^2+2$:

  

(e)

To determine

Make a table of values and draw the graph for the relation $x=-\frac{1}{2}{(y-2)}^2+3$ for integral values of y from -1 to 5.

Explanation of Solution

Calculation:

  $x=-\frac{1}{2}{(y-2)}^2+3$

Make a table:

y	$x=-\frac{1}{2}{(y-2)}^2+3$
-1	$-\frac{3}{2}=-1.5$
0	1
1	2.5
2	3
3	2.5
4	1
5	-1.5

Now , plot the above coordinates and join them to get the graph of relation $x=-\frac{1}{2}{(y-2)}^2+3$: