Question

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

r = -4 + 5 cos θ

Answer 1

if we do
f(-x)=f(x) then it is symetric about the y axis

if we do f(x)=-f(x) then it is symetric about the x axis

if we do f(-x)=-f(x) then it is symetric about the origin


if we graph it we see it is clearly symetric about the y axis
see, if we have x=pi and x=-pi, f(pi)=-1=f(-pi)
just like f(x)=f(-x)

it is symetric about the y axis

Answer 2

x-axis

Explanation:

sine is over the y - axis always unless it is a rose petal with an even number or petals, or a perfect circle

cos is always x- axis unless it is a rose petal with an even number or petals, or a perfect circle

because this is a limacon graph with an inner loop, it is only symetric over the x-axis!

hope this helps you understand better