Question

Identify the graph of the polynomial function $f$
$f\left(x\right)=x^3-2x^2-x+2$

• A. graph a
• B. graph b
• C. graph c
• D. graph d

Answer 1

The correct option is A graph a

Let $y=x^3-2x^2-x+2$

The graph of $f\left(x\right)$ in this example is the graph of $y=x^3-2x^2-x+2$. It is easy to generate points on the graph.

Choose a value for the first coordinate, then evaluate $y$ at that number to find the second coordinate.

The several values for $x$ and the function $y$ evaluated at those numbers.

If $x=0$, then $y=x^3-2x^2-x+2=(0{)}^3-2(0{)}^2-0+2=2$implies the point is $(0,2)$.

If $x=1$, then $y=x^3-2x^2-x+2=(1{)}^3-2(1{)}^2-1+2=1-2-1+2=0$implies the point is $(1,0)$.

If $x=-1$, then $y=x^3-2x^2-x+2=(-1{)}^3-2(-1{)}^2-(-1)+2=-1-2+1+2=0$implies the point is $(-1,0)$.

Hence, the graph of the function is shown above.