Question

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

r = -2 + 3 cos θ

Answer 1

x-axis only

Explanation:

Look at the graph

Answer 2

This equation is an example of a Limacon with inner loop. By using the symmetry tests where:

POLAR AXIS/HORIZONTAL:
replace a) θ by -θ, b) r by -r and θ by π-θ

VERTICAL AXIS:
replace a) θ by π-θ, b) r by -r and θ by -θ

POLE:
replace a) θ by π+θ, b) r by -r

If any of these rules, after replacing it in the equation, results to the original equation (making it the equivalent) then it is symmetrical to that axis.

In this case, it is only symmetrical about the polar/horizontal axis.