Question

Describe the symmetry, if any, of the graph of the function

x
f(x) = ____
x^2 + 5
.
A)
no symmetry
B)
origin symmetry
C)
x-axis symmetry
D)
y-axis symmtery
Eliminate

Answer 1

is your function like this:
\(y=x^2+5\)

Answer 2

Yes, clarity is an issue here.

Describe the symmetry, if any, of the graph of the function f(x) =

x+x^2 + 5 ??? Is that the function you're dealilng with?

Answer 3

i edit for u @Michele_Laino

Answer 4

hint:
if I make this transformation: \(x \rightarrow -x\), then the function \(f(x)\) will transform according this rule:
\[\Large f\left( { - x} \right) = \frac{{ - x}}{{{{\left( { - x} \right)}^2} + 5}} = - \frac{x}{{{x^2} + 5}} = - f\left( x \right)\]
so, what can you conclude?

Answer 5

hint:
when I can write such formula, namely \(f(-x)=-f(x)\), then I say that \(f(x)\) is an \(odd \) function
for example \(f(x)=x^3\) is an odd function, and its graph is like this:

Answer 6

i dont know i use math way

Answer 7

as we can see the function \(f(x)=x^3\), is symmetric with respect to the origin, since for any point \((x,y)\) I have its symmetric with respect to the origin:

so, what is the right option?