The degree of a polynomial function helps us to determine the number of
x -intercepts and the number of turning points. A polynomial function of
degree is the product of
factors, so it will have at most
roots or zeros, or
x -intercepts. The graph of the polynomial function of degree
must have at most
turning points. This means the graph has at most one fewer turning point than the degree of the polynomial or one fewer than the number of factors.
A
continuous function has no breaks in its graph: the graph can be drawn without lifting the pen from the paper. A
smooth curve is a graph that has no sharp corners. The turning points of a smooth graph must always occur at rounded curves. The graphs of polynomial functions are both continuous and smooth.
Intercepts and turning points of polynomials
A polynomial of degree
will have, at most,
x -intercepts and
turning points.
Determining the number of intercepts and turning points of a polynomial
Without graphing the function, determine the local behavior of the function by finding the maximum number of
x -intercepts and turning points for
The polynomial has a degree of
so there are at most 10
x -intercepts and at most 9 turning points.
Drawing conclusions about a polynomial function from the graph
What can we conclude about the polynomial represented by the graph shown in
[link] based on its intercepts and turning points?
The end behavior of the graph tells us this is the graph of an even-degree polynomial. See
[link] .
The graph has 2
x -intercepts, suggesting a degree of 2 or greater, and 3 turning points, suggesting a degree of 4 or greater. Based on this, it would be reasonable to conclude that the degree is even and at least 4.
What can we conclude about the polynomial represented by the graph shown in
[link] based on its intercepts and turning points?
The end behavior indicates an odd-degree polynomial function; there are 3
intercepts and 2 turning points, so the degree is odd and at least 3. Because of the end behavior, we know that the lead coefficient must be negative.
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature