Chapter 4.1, Problem 115AYU

To determine

To explain:

The general strategy for graphing a polynomial function, degree, intercepts, end behavior and turning points.

Answer to Problem 115AYU

All terms are explained.

Explanation of Solution

To graph a polynomial function, it is best to find different features as,

Degree: The degree of the polynomial function is the highest exponential value of the independent variable in the function.

The degree allows to know in a way how the polynomial will normally look when it gets graphed. Also, it tells us or show us the number of possible roots or the $x-$ intercepts.

  $x-$ intercepts:

The $x-$ intercept is where the function crosses the $y-$ axis on the coordinate plane.

  $y-$ intercepts: The $y-$ intercept is where the function crosses the $x-$ axis on the coordinate plane.

End behavior: The End behavior is telling that what the function does at the negative end and positive end graphically and mathematically.

Turning points: Number of local maxima and minima of the function.

Degree:

The degree shows that the good amount of information about the graph. Such as it shows that the general shape of the polynomial, like as does it start from the bottom and continue to the stop, or does it start at the top and curve its way to back at the top.

End Behavior:

The end behavior of a polynomial function is a description of how the polynomial behaves as it approaches positive and negative infinity.

Some have each end go to positive infinity. The end behavior is totally dependent on the leading term of the polynomial function when simplified.

  $X-$ intercept:

The $x-$ intercepts of a polynomial means where the polynomial intersects the $x-$ axis on the real coordinate plane.

  $Y-$ intercept:

The $y-$ intercepts of a polynomial means where the polynomial intersects the $y-$ axis on the real coordinate plane.

Turning points:

The turning points are extrema of function. The extrema are the minimum points and maximum points within the middle behavior of the polynomial. That is tops of the hills and bottoms of the valleys.