Chapter 6.4, Problem 49HP

To determine

To sketch:the graph of an odd polynomial function with 6 turning point and 2 double roots.

Answer to Problem 49HP

the function is odd degree, its end points are in opposite side.

The double roots mean that the graph will be twice tangent to $\text{x-axis}$ .

Finally count to have $\text{6}$ turning points.

Explanation of Solution

Given:

  $\text{f}\left(\text{x}\right){\text{=-2x}}^4{\text{+5x}}^{\text{3}}{\text{-4x}}^{\text{2}}\text{+3x-7}$ .

Concept used:

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

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

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

If the function is odd degree, its end points are in opposite side.

Calculation:

The graph of the odd function will be:

  

Graphing the given characteristics, the end behavior should go on opposite direction. The graph should be Intersects on the zeroes of the function.

Since the function is odd degree, its end points are in opposite side.

The double roots mean that the graph will be twice tangent to $\text{x-axis}$ .

Finally count to have $\text{6}$ turning points.