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What is the behavior of the function y=f(x) as x approaches infinity or x approaches negative infinity, is called the what of the function?
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Definition
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How do you find the degree of a polynomial?
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Definition
It is the largest exponent.
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When given a polynomial of this form, how are you supposed to look at it?
((Ax^B)+(Cx^D))/E
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Definition
(Ax^B/E)+(Cx^D/E)
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What is the leading term of this polynomial?
((Ax^B)+(Cx^D))/E
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Definition
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What is the leading coefficient of this polynomial?
((Ax^B)+(Cx^D))/E
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Definition
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Why is this function, not a polynomial function?
f(x)=(x^A)+B|x|-C
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Definition
The presence of |x|
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What is the "a" value of a function?
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Definition
The first coefficient, when the terms are listed in descending order.
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What is the "n" value of a function?
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Definition
The highest exponent of a function.
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What is the behavior of a graph with an "a" value that is larger than zero, and a "n" value that is even?
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Definition
It makes a W
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y approaches infinity as x approaches negative infinity
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y approaches infinity as x approaches infinity
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Term
What is the behavior of a graph with an "a" value that is less than zero, and a "n" value that is even?
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Definition
It makes an upside down W
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y approaches negative infinity as x approaches negative infinity
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y approaches negative infinity as x approaches infinity
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What is the behavior of a graph with an "a" value that is larger than zero, and a "n" value that is odd?
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Definition
It makes a W where the left side is reflected over the x-axis
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y approaches negative infinity as x approaches negative infinity
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y approaches infinity as x approaches infinity
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Term
What is the behavior of a graph with an "a" value that is less than zero, and a "n" value that is odd?
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Definition
It makes a W where the right side is reflected over the x-axis
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y approaches infinity as x approaches negative infinity
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y approaches negative infinity as x approaches infinity
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What is the y-intercept of this polynomial function?
f(x)=(x^A)-(Bx^C)+D
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Definition
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How do you find the zeroes of this function?
f(x)=((x-A)^B)(x+C)^D
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Definition
The zero of factor ((x-A)^B) is "A"
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The zero of factor (x+C)^D is "-C"
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How do you find the multiplicities of this function?
f(x)=((x-A)^B)(x+C)^D
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Definition
The multiplicity of factor ((x-A)^B) is "B"
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The multiplicity of factor (x+C)^D is "D"
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How do you find whether the graph of this function crosses, or touches but does not cross, the x-axis at each x-intercept?
f(x)=((x-A)^B)(x+C)^D
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Definition
If a multiplicity is odd, it crosses at the x-axis
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If a multiplicity is even, it touches at the x-axis
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How do you find the maximum number of turning points for this function?
f(x)=((x-A)^B)(x+C)^D
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Definition
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How do you find the the degree of this function?
f(x)=((x-A)^B)(x+C)^D
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Definition
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How do you find the zeroes of this polynomial?
f(x)=(x^3)-(Bx^2)+Cx
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Definition
One of your zeroes is 0, the other two are the factors that multiply to equal C, and are added together to equal B, but with opposite signs.
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Term
How do you test to find at what interval the graph is below the x-axis?
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Definition
Your intervals are:
(-Infinity,Lowest Zero),
(Lowest Zero, Highest Zero),
(Highest Zero, Infinity)
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Pick a value from each interval and plug it into the function.
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If a value produces a positive solution, then that interval is above the x-axis, if not then that interval is below the x-axis.
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Term
How do you test to find at what interval the graph is above the x-axis of this problem?
f(x)=(x^2)+Ax-B
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Definition
It's probably
(-Infinity,Lowest Zero)
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(Highest Zero, Infinity)
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Term
How do you test to find at what interval the graph is below the x-axis of this problem?
f(x)=(x^2)+Ax-B
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Definition
It's probably
(Lowest Zero, Highest Zero)
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Term
What is the y-intercept of this function?
f(x)=(x^2)+Ax-B
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Definition
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How does one find symmetry about the vertex of a parabola based on this function?
f(x)=(x^2)+Ax-B
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Definition
a= The coefficient of the first term
b= B
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x = -b/2a
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