Question

for the given equation list the intercepts and test for symmetry
y=-x^7/x^6-8

Answer 1

Just to be clear
\[y = \frac{-x^{7}}{x^{6}-8}\]
is this it?

Answer 2

yes

Answer 3

To get y-intercepts, take
x=0, see what values you get for y.
To get x-intercepts, take
y=0, see what values you get for x.

By symmetry, did you mean symmetry with respect to the y-axis?

Answer 4

Yes thank you for the help

Answer 5

Well, to test symmetry with respect to the y-axis, take a random positive value
for x
x = a, for instance.

then
\[y = \frac{-a^{7}}{a^{6}-8}\]

Now test
x = -a
if you get the same value for y, as you did for x = a, then
the graph is symmetrical with respect to the y-axis :)

Answer 6

thanks my brain gets rusty

Answer 7

No problem :)