End Behaviors & Degree
What's the value of a?
X and Y intercepts
Write the equation
Zeros & Multiplicity
Domain and Range
100
What is the degree and end behavior?
f(x) = -x^4 + x^2 -x -3
Degree: 4
As x -> -inf y -> - inf
As x -> inf y -> -inf
100
The function
y = a(x-2)(x+3)
through the point (1, -16).
a = 4
100
Find the zeros of the function: y = (x - 3)(x + 2)
x = -2 or 3
(-2, 0), (3, 0)
100
Decide if the value of a is + 1 or -1
y=(x+4)(x+1)(x-1)(x-3)
100
Find the zero(s) and the multiplicity for each zero
f(x)= x^2 - 4
x = 2 and -2, both multiplicity of 1
100
Find the domain and range
D: {-7, -4, -2, 8, 10, 19}
R: {-11, -5, 6, 9, 12, 17}
200
What is the degree and end behavior?
f(x)=-5x^5+3x^3-3x+1
5
As x -> -inf y -> inf
As x -> inf y -> -inf
200
The function
g(x) = a(x-4)(x+2)(x-1)
through the point (2, -16).
a = 2
200
What are the x and y-intercepts of this function
f(x)=sqrt(x+4)-5
x-intercept: (21,0)
y-intercept: (0,-3)
200
Decide if the value of a is + 1 or -1
-(x+3)^2(x-5)
200
Find the zero(s) and the multiplicity for each zero
f(x) = x^2 + 10x + 25
zero:x=-5 multiplicity of 2
200
Find the domain and range.
D: (-12, 6]
R: (-8, 16]
300
What is the end behavior and degree of the function?
f(x)=(x-3)(x+6)(x-8)^2
Degree: 4
As x -> -inf y -> inf
As x -> inf y -> inf
300
The function
y=a(x-3)^2(x+2)
through the point (2, -8).
a = -2
300
Find the zeros of the function: y = x(x + 1)(x - 7)
x = 0, -1 and 7
(0,0), (-1, 0) (7,0)
300
Decide if the value of a is + 1 or -1
(x+4)(x+2)(x-3)^2
300
x = -3 (multiplicity 1)
x = 2 (multiplicity 2)
x = 5 (multiplicity 1)
300
Find the domain and range of the function.
D: [-inf, inf]
R: [0, inf]
400
What is the end behavior and degree of the function?
f(x) = (x-3)^2(x+4)(x-1)^2
Degree: 5
As x -> -inf y -> - inf
As x -> inf y -> inf
400
Double jeopardy!
The function
g(x)=a(x-5)^2(x+2)^2
through the point (4, 18).
a = 0.5
400
Find the x and y intercepts of the function
y=x^2(x-3)(x+4)
x-intercepts
(0,0), (3,0) (-4,0)
y-intercept
(0,0)
400
Decide if the value of a is + 1 or -1
g(x)= -x(x+2)(x-2)^2
400
x = -1 (multiplicity 2)
x = 2 (multiplicity 3)
x = 4 (multiplicity 1)
400
Find the domain and range of the function.
D: (-inf, inf)
R: (-inf, 5]
500
What is the degree and the end behaviors of the function?
f(x) = -2x(x+3)(x-8)^2
Degree: 4
As x -> -inf y -> - inf
As x -> inf y -> -inf
500
The function
y = a(x+3)^2(x-2)^2(x+5)
through the point (-2, -24).
a = -0.5
500
Find the x and y intercepts of the function
y=x^2+25
No x-intercepts
Y-intercept (0,25)
500
Write a polynomial equation for a graph that passes through the point (1, 56) and has three x-intercepts: (–3, 0), (2, 0), and (5, 0).
y = 3.5(x + 3)(x − 2)(x − 5)
500
Find a polynomial function leading coefficient of -2 and with given zeros and multiplicity : zero: -5, multi: 3 | zero:0 , multi:2
y = -2x^2(x+5)^3
500
Find the domain and range
D: (-inf, 2)
R: (-inf, 0)