Question

Find the intercepts of function f(x) = -x³ / x²+9 ​

Answer 1

Answer:

x-intercept (0,0)

y-intercept (0,0)

Step-by-step explanation:

The given function is

$f(x) = \frac{ - {x}^{3} }{ {x}^{2} + 9}$

To find the x-intercept, we substitute y=f(x)=0

This implies that:

$\frac{ - {x}^{3} }{ {x}^{2} + 9 } = 0$

$- {x}^{3} = 0 \cdot( {x}^{2} + 9)$

$- {x}^{3} = 0$

${x}^{3} = 0$

$x = 0$

Therefore the x-intercept is (0,0)

To find the y-intercept we substitute x=0

$f(0) = \frac{ - {0}^{3} }{ {0}^{2} + 9 }$

$f(0) = \frac{0}{9} = 0$

The y-intercept is (0,0)