Chapter 6.4, Problem 28PPS

To determine

To sketch: the polynomial even function having zeros at $-2,1,3\text{}\text{and 5}\text{.}$ .

Answer to Problem 28PPS

Graphing the given characteristics, the end behavior should be on the same direction going up and the graph should intersect on the zeroes given.

Explanation of Solution

Given:

An even function with zeroes at:

  $-2,1,3\text{}\text{and 5}\text{.}$

Concept used:

The graph of the function $\text{f}$ is the set of all point in the plane of the form $\left(x,f\left(x\right)\right)$ .

The graph can be defined by the graph of $\text{f}$ and the equation for the graph will be $y=f\left(x\right)$ .

The graph of the function is special case of the graph of an equation.

When factors are multiplied each other.

It can generate equation which can be plot in the graph using graphing calculator like Desmos graphing calculator.

If the function is even then the end point of graph will be in same direction.

Calculation:

An even function with zeroes at:

  $-2,1,3\text{}\text{and 5}\text{.}$

Then its factor will be:

  $\left(x+2\right)\left(x-1\right)\left(x-3\right)\left(x-5\right)$ .

The graph of an even function will be:

Graphing the given characteristics, the end behavior should be on the same direction going up and the graph should intersect on the zeroes given.