Q6. - Algebra 2

Question

Determine consecutive values of x between which each real zero of each function is located. Then draw the graph.

 

$f\left(x\right)=x^3-x^2+1$

Step-by-Step Solution

Answer

The consecutive values of x between which each real zero of the function is located are -1 and 0.

Step 1. Given Information.

Given to determine the consecutive values of x between which each real zero of the function $f\left(x\right)=x^3-x^2+1$ is located. Then the graph needs to be drawn. 

Step 2. Explanation .

The real zero of a function lies where the value of the function changes from positive to negative or negative to positive.

So, making a table of values of the function:

x	f(x)
-2	-11
-1	-1
0	1
1	1
2	5

Here the value of the function changes only once between -1 and 0.

Graphing the function using the values in the table:

Step 3. Conclusion .

Hence the consecutive values of x between which each real zero of the function is located are -1 and 0.