Answer:
x-intercept (0,0)
y-intercept (0,0)
Step-by-step explanation:
The given function is
[tex]f(x) = \frac{ - {x}^{3} }{ {x}^{2} + 9} [/tex]
To find the x-intercept, we substitute y=f(x)=0
This implies that:
[tex] \frac{ - {x}^{3} }{ {x}^{2} + 9 } = 0[/tex]
[tex] - {x}^{3} = 0 \cdot( {x}^{2} + 9)[/tex]
[tex] - {x}^{3} = 0[/tex]
[tex] {x}^{3} = 0[/tex]
[tex]x = 0[/tex]
Therefore the x-intercept is (0,0)
To find the y-intercept we substitute x=0
[tex]f(0) = \frac{ - {0}^{3} }{ {0}^{2} + 9 } [/tex]
[tex]f(0) = \frac{0}{9} = 0[/tex]
The y-intercept is (0,0)
