End Behavior
What is the end behavior of f(x)=3x4?
As x approaches infinity, f(x) approaches infinity.
As x approaches negative infinity, f(x) approaches infinity.
*cannot use device for this; use graphing calculator
What is the domain and range of the function f(x)=5x8?
Domain: All real numbers
Range: y≥0
Find the degree and leading coefficient of f(x)=7x2-4x5+3x+2.
Degree: 5
Leading Coefficient: -4
For f(x)=x-2.5, identify the consecutive integer interval that contains the zero.
x=2 to x=3
Simplify: x(3x+4)
3x2+4x
Terrific Triple!!! **The team that chose this problem will earn triple points if they get it correct**
What is the end behavior of g(x)=-5x3?
As x approaches infinity, f(x) approaches negative infinity.
As x approaches negative infinity, f(x) approaches infinity.
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*cannot use device for this; use graphing calculator
What is the domain and range of g(x)=-2x3?
Domain: All real numbers
Range: All real numbers
What is the degree and leading coefficient of g(x)=-3x5+2x4+2x7+x
Degree: 7
Leading Coefficient: 2
For f(x)=x2+2x-5, identify the consecutive integer interval that contains the zero.
x=-4 to x=-3
x=1 to x=2
Multiply and simplify: x(3x-5)(5x-4)
15x3-37x2+20
What is the end behavior of h(x)=2x7?
As x approaches infinity, f(x) approaches infinity.
As x approaches negative infinity, f(x) approaches negative infinity.
*cannot use device for this; use graphing calculator
State the domain and range of h(x)=4x10.
Domain: All real numbers
Range: y≥0
Terrific Triple!!! **The team that chose this problem will earn triple points if they get it correct**
Identify the degree and leading coefficient of h(x)=4x-2x4+3x2+8-5x8.
Also find the value if x=3.
Degree: 8
Leading Coefficient: -5
f(3)= -32,920
Terrific Triple!!! **The team that chose this problem will earn triple points if they get it correct**
For f(x)=x3+4x2-2, identify the consecutive integer interval that contains the zero.
x=-4 to x=-3
x=-1 to x=0
x=0 to x=1
**Steal from a team! If the team that chose this problem answers it correctly, they can steal 200 points from the team of their choice, in addition to earning the double points for getting the right answer.***
Divide (24a8b5c4 - 32a4b2c + 4a2b2) by (4a2b2)
6a6b3c4 - 8a2c + 1
A polynomial has an odd degree and a negative leading coefficient. What is its end behavior?
As x approaches infinity, f(x) approaches negative infinity.
As x approaches negative infinity, f(x) approaches positive infinity.
Terrific Triple!!! **The team that chose this problem will earn triple points if they get it correct**
What is the domain and range of f(x)=-4x6?
Domain: All real numbers
Range: y≤0
**Steal from a team! If the team that chose this problem answers it correctly, they can steal 200 points from the team of their choice, in addition to earning the double points for getting the right answer.***
Identify the degree and leading coefficient of f(x)=-2x3+2x4-x5+x+2.
Also identify the value when x=2.
Degree: 5
Leading coefficient: -1
f(2)= -12
For f(x)=2x5+3.8x4-1.2, identify the consecutive integer interval that contains the zero.
x= -2 to x= -1
x= -1 to x=0
x=0 to x=1
Terrific Triple!!! **The team that chose this problem will earn triple points if they get it correct**
A box has the following dimensions: height of 2x, width of (2x+7), and a length of (5x-1). What is the volume of the box?
Hint: V=w*l*h
20x3+66x2-14x
What is the end behavior of f(x)=-4x6+7x2-1?
As x approaches infinity, f(x) approaches negative infinity.
As x approaches negative infinity, f(x) approaches negative infinity.
How is the range of f(x)=x6 different from the range of g(x)=x5?
The range of f(x) is y≥0, while the range of g(x) is all real numbers.
A polynomial has degree 9 and leading coefficient 2. What term must appear in the polynomial, and why?
Additionally, write down a term that cannot be in this polynomial and why.
The term 2x9 has to appear.
Answers vary for the second part.
For f(x)=x5 -4x3+3x2 -8x-6, identify the consecutive integer interval that contains the zero.
x= -3 to x= -2
x= -1 to x=0
x= 2 to x=3
Divide (18x6y4 - 6x4y3 + 12x5y2) by (6x3y2)
3x3y2 -xy + 2x2