Question

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

Answer 1

Answer:

Attachment

Step-by-step 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.