Change
ROC Linear Functions
Polynomial Functions and ROC
Complex Zeros
End Behavior
100
The average rate of change of the quadratic function p is -4 on the interval 0≤x≤2 and -1 on the interval 2≤x≤4. What is the average rate of change of p on the interval 6≤x≤8 ?
5
100
Two points are given: (0, 30), (12, 100)
If the line that crosses these points is constant, what is the rate of change?
5.83 (70/12)
100
Classify the polynomial by degree and number of terms:
-3x3
Quartic Monomial
100
Is the function f(x) = 5x7-5x3 even or odd?
Odd
100
The function f is given by 4x6-3x3+2. Describe the end behavior of f.
As input values decrease, the function increases and as input values increase, the function increases.
200
x : -3 3 6
f(x): -10 -2 2
The table gives values of the function f for selected values of x. If the function f is linear, what is the value of f13 ?
34/3
200
If: x(0, 2, 5, 6, 8, 15, 17) and y(1, 4, 3, 7, 10, 12, 15) What is the slope of the graph?
(y = 0.8x + 1)
200
Find all real solutions for the polynomial: 2x3-4x2-6x=0
{0, -1, 3}
200
Given the polynomial function f(x) = 3x2+2x-1, what are all intervals on which f(x) < 0?
(-1, 1/3)
200
The function h is given by h(x)=-3x5-4x3+2x2-10. Describe the end behavior of h as the input values increase without bound.
lim h(x) = -∞
x->∞
300
The graph of the function f is given for -3≤x≤6. Which of the following statements about the rate of change of f over the interval 2<x<6 is true?
A. The rate of change is positive.
B. The rate of change is negative.
C. The rate of change is increasing.
D. The rate of change is decreasing.
D. The rate of change is decreasing.
300
The line is concave up and increasing and goes from the origin to the point (130, 60) [minutes, miles] What is the linear rate of change in [hours, miles]?
27.69 (360/13)
300
Classify the polynomial by degree and number of terms and solve:
2x3-7x2+8
Cubic Trinomial {-0.712, 4.212}
300
Given the zero x = 2+3i, what are the other zeros of the polynomial function g(x) = x3-8x2+29x-52?
x=2-3i, x=4
300
For polynomial function g,
lim g(x) = ∞ and lim g(x) = -∞
x->-∞ x->∞
What is true about the function g of its degree and leading coefficient?
g is a odd function with a negative leading coefficient
400
A linear function P is used to model the price, in dollars, of used cars as a function of their age t, in years. It is known that P4=7300 and P7=5500. Based on this model, which of the following is true?
A. For each year that a car ages, its price decreases by approximately 25%.
B. For each year that a car ages, its price decreases by approximately 75%.
C. For each year that a car ages, its price decreases by approximately $600.
D. For each year that a car ages, its price decreases by approximately $1800.
C. For each year that a car ages, its price decreases by approximately $600.
400
From the absolute extremas, find the rate of change of function f(x)=4x5+9x2+3x with the restricted domain of -1 < x < 0
-3.375
400
What is the Rate of Change of f(x)=2x2-3x+5 over the interval 2<x<5?
11, (2,7) (5,40)
400
The leading term of the polynomial function p is axn, where an is a real number and n is a positive integer. The factors of p include (x-1), (x+i), and (x-(5+i)). What is the least possible value of n?
5
400
A polynomial function f is given by
f(x) = axb where a is an integer and b is a positive integer. It is known that
lim f(x) = ∞ and lim f(x) = ∞
x->-∞ x->∞
What is true about the value of b in relation to the end behavior?
b is an even number
500
The electromagnetic force between two particular particles is related to the distance between the particles. This relationship is modeled by the function F, where Fd=3.6d2 for distance d, measured in centimeters, and force Fd, measured in Newtons. What is the average rate of change, in Newtons per centimeter, in the electromagnetic force if the distance between two particles is increased from 2.3 centimeters to 3.1 centimeters?
-0.382
500
The volume of a spherical balloon is determined by V(r)=4/3πr3; the volume is determined by the change in radius(r). r changes from 6 to 2.5, what is the average rate of change in the balloon’s volume?
m=(y2-y1)/(x2-x1)):
(V(6) - V(2.5)) / (6 - 2.5) = 76.31
500
What is the Rate of Change of 4x4+2x3-8x2-2x-1 over interval 0.5<x<1.5?
8.5 (0.5, -3.5) (1.5,5)
500
Function g is given by g(x) = 6x4-x3+4x2-x-2. What is the maximum number of non-real zeros possible for the function f?
2 non-real zeros
500
The function h is given by
h(x) = (3x2-2x+4)/(x2-1). Describe the end behavior as the input values decrease without bound using limit notation.
lim h(x) = 1
x->-∞