Rate of change
Polynomials
Rational Functions
Polynomials and Rational Functions
Misc.
100
Find the interval where f(x) is concave up. Justify your answer.
f(x) is concave up on (1, 4) because the average rates of change are increasing.
100
What is the degree of the following function?
6x^7+3x^8-2x^2
8
100
What is the end behavior of the following function?
(4x^3+2x^2-7)/(5x^3+6)
100
Horizontal Asymptote: Yes or No?
h(x) = (5x3-2x2-1)/(x4-6)
If yes, Equation:
yes!
y = 0
100
On what open intervals is k(x) both increasing and concave down? 
(-6,-3)
200
What is the leading coefficient and degree of g(x)=-3x2+5x-8x4-2
LC = -8
Degree = 4
200
Use the limit definition to state the end behavior of the polynomial functions.
f(X)= -8x^7+3x^2+5
200
Find the horizontal asymptote of
(x^3+x^2-9)/(x^5-3x^2-5x)
y = 0
200
What is the end behavior of a polynomial with a positive leading coefficient and odd degree?
As lim x-> infinity = infinity; lim x-> -infinity = infinity
200
Calculate the average rate of change of the function π(π₯) =
x^2-9x
in the interval 2 β€ π₯ β€ 7.
0
300
The table gives values of a function f for selected values of x. Is the function linear or quadratic? Justify your choice?
f(x) is quadratic; f(x) has a constant second difference over equal-length input value intervals OR the rates of change are changing at a constant rate.
300
Where is the relative maximum of the function? (Calc. okay)
h(x)=2x^3-4x
(-0.816, 2.177)
300
Find the zeros of the function.
(4-x^2)/(x-2)
-2
300
Use the binomial theorem to expand
(2x-1)4
16x4-32x3+24x2-8x+1
300
What is the third term: (2x -3)6 ?
2160x4
400
Let
f(x)=x2-4
The average rate of change of over the interval [c, 5] is equal to 3, where c is a constant. Find the value of c.
c = -2
400
Let π π be a polynomial function with the given values. Are there any guaranteed extrema? If so, state where they occur. (State the interval where it occurs)
A) π(-1)= 0, π(0)= 10, and π(10)= 0.
B) π(-9)= 7, π(0) = 4, and π(5)= 0
a) Yes, on -1<x<10
b) No guarantee
400
Find the zeros, vertical asymptote and holes if any.
zero x = 8 (8, 0)
VA x = 0, x = 1
Hole x = -2
400
What is the slant asymptote of:
f(x) = (4x3-5x+1)/(2x2+3x)
y = 2x - 3
400
What is the domain of a function:
(x-3)/(x2-3x)
(-infinity, 0] U [0,3] U [3, infinity)
500
What is the average rate of change of f(x)= 5x-4x2
-8?
500
Which of the following statements are true about the polynomial function p(x)?
The degree of p(x) is even.
The degree of p(x) is at least 6.
p(x) has four real zeros.
500
Solve the following inequality. Answer using interval notation.
(-β,4/3] βͺ(-1,2]
500
Given:
(x2+8x+12)/(x2-4)
a) Write in Factored form.
b) Identify the zero(s) and hole
c) Identify the vertical asymptote
d) Domain
e) Horizontal Asymptote
a) [(x+2)(x+6)]/[(x+2)(x-2)]
b) zero: x = -6 hole: x = -2
c) VA: x = 2
d) Domain: (-inf, -2]U [-2, 2] U [2, inf)
e) HA: y= 1
500
Write the rational function with the following properties:
The graph of f has a hole at x=2, and vertical asymptotes at x=3 and x=-5.
(x-2) / ((x-2) (x-3) (x+5))