Question

Solve the equation graphically in the given interval. State each answer rounded to two decimals

$x^{\frac{1}{3}}-x=0;$$\left[-3,3\right]$

Short answer

The solution by graphically method is $x\approx -1,0,-1$.

Step-by-step solution

Step 1. Definition of the x-intercept.

x-intercept is the point where the value of y is 0.

Step 2. Draw the graph of the equation.

$x^{\frac{1}{3}}-x=0$;$\left[-3,3\right]$

Now, equate the left side of the equation to$y$Then sketch the graph of the equation on a graphing facility

Draw the graph:

Step 3. Solve the equation graphically.

The solutions to the given equations are the x-intercepts or the zeros of the graph.

So, identify the values of x-intercepts by using the trace function of the graphing utility.

Hence, the solutions or the zeros are$x=-1,0,$ and $1$.