Q. 22 - Calculus

Question

For each of the following sign charts, sketch the graph of a function f that has the indicated signs, zeros, and discontinuities:  

Step-by-Step Solution

Answer

The graph of a function f that has the indicated signs, zeros, and discontinuities is   

Step 1. Given Information.

The given sign chart is

Step 2. Sketch the graph.

The graph has four zeros which are $-4, -2, 0 \mathrm{and} 2.$

From the sign chart, we can depict that the graph is positive in the interval negative infinity to $-4$ and in the interval $\left[0, 2\right]$. The graph is negative in the interval $\left[-4, -2\right],\left[-2,0\right] \mathrm{and} \left[2,\infty \right].$ The graph is discontinuous at $x=2 a\mathrm{nd} x=-2.$