Polynomial and
Rational
Functions
Rational
Functions
Rational Functions and their Graph
Polynomial and Rational Inequalities
Combination and Composition of Functions
Inverse Functions
100
The behavior of the graph of a polynomial function to the far left or the far right is called its ____ behavior.
And it depends upon the ____ term(s)
End, leading
100
Find the domain of the following rational function.
The domain of f(x) is restricted to
(-∞,9)U(9,∞)
100
Use the graph of the function f to solve the inequality.
(a) f(x)< 0
(b) f(x)>0
(a).
(b).
100
For f(x)=√x and g(x)= x- 6, find the following function.
100
Does the graph represent a function that has an inverse? (Use the Horizontal Line Test)
Yes. (Horizontal line hits the graph ONLY once)
200
Fill in the blanks so that the resulting statement is true
The graph of f(x)=x3_____ to the left and ______to the right
The graph of f(x)=x3 Falls to the left and Rises to the right
200
Find the vertical asymptotes, if any, of the graph of the rational function.
The vertical asymptotes are
x=0,x=7
200
Solve the polynomial inequality. Identify the Intervals and their sign. Write the solution set in interval notation.
x2-8x+16<0
Intervals = (-∞,-4) (-4,8)
Sign = +++ +++
Solution set = The solution set is EMPTY
200
For f(x)=2x2-9x+10 and g(x)= x-2, find the following function.
(fg)(x)=
(fg)(x)=2x3-13x2+28x-20
200
Find the f(g(x)) and g(f(x)) and determine if they are inverses of each other
f(x)=7x and g(x)=x/7
They are inverses of each other
(x)=x and g(x)=x
300
Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function.
f(x)=4x4+7x3-x+9
The graph of f(x) rises to the left and rises to the right
300
Use the graph of the rational function to complete the following statement.
As x→-1-, f(x)→___
f(x)→∞
300
Solve the Rational Inequality, Identify the Intervals and their sign. Write the solution set in interval notation.
Intervals
--- +++ --- +++
Solution Set:
300
For f(x)=2x2-9x+10 and g(x)= x-2, find the following function.
(f/g)(x)=
(f/g)(x)= 2x-5
300
Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other.
f(g(x)) =
g(f(x)) =
f(g(x)) =x
g(f(x)) =x
400
Use the leading coefficient test to determine whether y → ∞ or y → -∞ as x → -∞ for
y= -14x4-10x3
Answer: y → -∞
400
Find the horizontal asymptote, if any, of the graph of the rational function.
The horizontal asymptote is
y=-7/5
400
Solve the polynomial inequality. Identify the Intervals and their sign. Write the solution set in interval notation.
(x-3)2(x-4)(x-7)2 ≤ 0
Intervals = (-8,3) (3,4) (4,7) (7,∞)
- - - - - - +++ +++
Solution set = [4,7] U [7,∞)
400
Find (f ◦ g)(x)=
Write the domain in interval notation.
(f ◦ g)(x)= 10-x
The domain is (-∞,6]
400
The function 
is one-to-one
Find an equation for f-1(x) the inverse function
500
Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around at each zero. f(x)=2(x+7)(x+6)2
The zeros are -7,-6. There are two zeros. The multiplicity of the smallest zero is 1, the largest is 2. The graph crosses at -7 and touches and turns around at -6
500
Find the horizontal asymptote, if any, of the graph of the rational function.
y=15/8
500
Solve the polynomial inequality. Identify the Intervals and their sign. Write the solution set in interval notation.
Intervals:
+++ --- +++ +++
500
Find (f ◦ g)(7)=
(f ◦ g)(7)=3
500
Given the function f(x)=x2-20, x≥0
Find an equation for f-1(x)
