Q. 3

Question

Test the equation $y = 5 x^{2} - 1$ for symmetry with respect to the x-axis, the y-axis, and the origin.

Step-by-Step Solution

Verified

Answer

The graph of the equation is not symmetric with respect to the x-axis.

The graph of the equation is symmetric with respect to the y-axis.

The graph of the equation is not symmetric with respect to the origin.

1Step 1: Given Information

Test the equation $y = 5 x^{2} - 1$ for symmetry with respect to the x-axis, the y-axis, and the origin.

2Step 2: x axis symmetry

To test for symmetry with respect to the x-axis, replace y by -y

$y = 5 x^{2} - 1 - y = 5 x^{2} - 1 i s n o t e q u i v a l e n t t o y = 5 x^{2} - 1$

The graph of the equation is not symmetric with respect to the x-axis.

3Step 3: y-axis symmetry

To test for symmetry with respect to the y-axis, replace x by -x.

$y = 5 x^{2} - 1 R e p l a c e x w i t h - x y = 5 {(- x)}^{2} - 1 y = 5 x^{2} - 1 i s e q u i v a l e n t t o y = 5 x^{2} - 1$

The graph of the equation is symmetric with respect to the y-axis.

4Step 4: symmetric about origin

To test for symmetry with respect to the origin, replace x by -x and y by -y

$y = 5 x^{2} - 1 R e p l a c e x w i t h - x a n d y w i t h - y - y = 5 {(- x)}^{2} - 1 - y = 5 x^{2} - 1 i s n o t e q u i v a l e n t t o y = 5 x^{2} - 1$

The graph of the equation is not symmetric with respect to the origin.

Q. 2

Q. 4

Other exercises in this chapter

Q. 1

The interval (2, 5) can be written as the inequality ___________

View solution

Q. 2

The slope of the line containing the points (-2, 3) and (3, 8) is ________.

View solution

Q. 4

Write the point–slope form of the line with slope 5 containing the point (3, -2).

View solution

Q. 5

The intercepts of the equation y=x2-9 are

View solution