Question

Graph the polynomial function $f\left(x\right)=x^3-x^2-4x+4$ by making table of values.

Short answer

The graph of the polynomial function $f\left(x\right)=x^3-x^2-4x+4$ is shown below.

Step-by-step solution

Step 1. Write down the given information.

The given polynomial function is $f\left(x\right)=x^3-x^2-4x+4$

Step 2. Construct the table of values.

Construct the table of values for different $x\text{and}y$ for the function $f\left(x\right)=x^3-x^2-4x+4$.

x	f(x)
1	0
2	0
-2	0
0	4
-1	6

Step 3. Sketch the graph of the function.

The graph of the function $y=-x^2+6x-5$ can be constructed by plotting the ordered pair of $\left(x,y\right)$ from the table.

Step 4. Interpretation the graph of the function.

From the graph it can be interpreted that the graph cuts x-axis at three points. Hence it will have three real solutions.