Question

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

Answer 1

x-intercept (0,0)

y-intercept (0,0)

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) = (0)/(9) = 0`

The y-intercept is (0,0)