Question

Which is the correct graph of f(x) = x3 – 10x2 + 9x ?

Answer 1

Attachment

Explanation:

Given:
`f(x)=x^3-10x^2+9x`

This is cubic equation. We will find x and y intercept.

For x-intercept: Put y=0

`x^3-10x^2+9x=0`

`x(x^2-10x+9)=0`

`x(x-9)(x-1)=0`

`x=0,1,9`

x-intercepts: (0,0) (1,0) (9,0)

For y-intercept: Put x=0

`f(0)=0^3-10\cdot 0^2+9\cdot 0=0`

y-intercept: (0,0)

End behavior : It is cubic equation and leading coefficient is 1.

Leading coefficient of is positive.

So, x → ∞ , y → ∞ and x → -∞ , y → -∞

Now, we will draw the graph using points and end behavior.

Please find attachment for graph.