Question

Graph the polynomial function $f\left(x\right)=x^4-7x^2+x+5$ by making table of values.

Short answer

The graph of the polynomial function $f\left(x\right)=x^4-7x^2+x+5$ is shown below.

Step-by-step solution

Step 1. Write down the given information.

The given polynomial function is $f\left(x\right)=x^4-7x^2+x+5$

Step 2. Construct the table of values.

Construct the table of values for different $x\text{and}y$ for the function $f\left(x\right)=x^4-7x^2+x+5$.

x	f(x)
0	5
1	0
-2.576	0
-0.813	0
2.388	0

Step 3. Sketch the graph of the function.

The graph of the function $f\left(x\right)=x^4-7x^2+x+5$ 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 four points. Hence it will have four real solutions.