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.
what's the difference between a firm and an industry
Abdul
firm is the unit which transform inputs to output where as industry contain combination of firms with similar production 😅😅
Abdulraufu
Suppose the demand function that a firm faces shifted from
Qd 120 3P
to
Qd 90 3P
and the supply function has shifted from
QS
20 2P
to
QS
10 2P .
a) Find the effect of this change on price and quantity.
b) Which of the changes in demand and supply is higher?
Demand curve shows that how supply and others conditions affect on demand of a particular thing and what percent demand increase whith increase of supply of goods
Israr
Hi Sir please how do u calculate Cross elastic demand and income elastic demand?
Abari
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