Question

Identify the graph of the polynomial function $f$
$f\left(x\right)=x^3-x^2+x-1$

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

Answer 1

The correct option is D graph d

Let $y=x^3-x^2+x-1$

The graph of $f\left(x\right)$ in this example is the graph of $y=x^3-x^2+x-1$. 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 $y=x^3-x^2+x-1=(0{)}^3-(0{)}^2+0-1=0-0+0-1=-1$implies the point is $(0,-1)$.

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

If $x=-1$, then $y=x^3-x^2+x-1=(-1{)}^3-(-1{)}^2-1-1=-1-1-1-1=-4$implies the point is $(-1,-4)$.

Hence, the graph of the function is shown above.