M1111-CH-3
Chapter Three:
Polynomial Function
3.1: Quadratic Functions and Models
Definition:
Let a, b, and c be real numbers with a 0. The function
f (x) = ax2 + bx + c
is called a quadratic function.
All quadratic functions have graphs that are U-shaped
Name: _ Date: _
1. Given x 2 + y 2 = 9 , use the algebraic tests to determine symmetry with respect to both axes and the
origin.
A) y-axis symmetry only
B) x-axis symmetry only
C) origin symmetry only
D) x-axis, y-axis, and origin symmetry
E) no symmetry
Name: _ Date: _
1. Find the distance between the points. Round to the nearest hundredth, if necessary.
(3, 9), (6, 5)
A) 5
B) 14.32
C) 16.64
D) 9.85
E) 6.08
2. Determine the quadrant(s) in which (x, y) is located so that the condition is satisfied.
x = 2
Name: _ Date: _
1. Evaluate the expression.
69
A)
B)
C)
D)
E)
54
3
15
3
15
2. Use inequality notation to describe the set.
all v in the interval [4, 20]
A) 4 < v < 20
B) 4 < v 20
C) 20 v 4
D) 4 v 20
E) 20 < v < 4
3. Which graph represents the interval?
(,
Name: _ Date: _
1. Simplify the expression.
4
w
A)
3
2
w
48
B)
w5
256
C)
w5
256
D)
w6
48
E)
2
w6
68
w6
2. Evaluate the expression.
(32 )
3
A) 3
B) 18
C) 729
D)
1
729
E)
1
729
Page 1
3. Rationalize the numerator. Then simplify your answer.
7 1
5
A) 6
M1111-CH-4
Chapter Four: Rational Functions
4.1: Rational Functions and Asymptotes
A rational function is a function that can be written in form:
f (x) =
N(x)
D(x)
2x + 1
Consider f (x) = x 1
D(x) 0
[-6, 6]1; [-4, 6]1
Definition of Vertical and Horizontal
Math 1111 Selected Solutions Chapter 1
Section 1.1
10. The x-intercept is (3,0) and the y-intercept is (0,9) .
12. The x-intercept is (1,0) and the y-intercepts are (0,1) and (0,1) .
54. r = (3 + 1)2 + (2 1)2 = 42 + 32 = 16 + 9 = 25 = 5
h =3
k = 2
Equatio
M1111-CH-P
Chapter P:
Section P.1:
Prerequisites
Review of Real Numbers and their Properties
Real Numbers represented by symbols:
Set of Real Numbers:
Whole
Integers
9, 0, , -0.66, ,
Rational
Irrational
Real Number Line
Negative
Direction
Positive
Directi
M1111-Ch-2
Chapter 2:
Functions and Their Graphs
2.1: Linear Equations in Two Variables
y = 2x + 1
x y
Slope-Intercept form of the Equation of a Line:
y = mx + b
Def: The slope of a line passing through two points
The slope of the nonvertical line through
Name: _ Date: _
1. Find the greatest common factor of the expression.
12y9u9, 90y3u6, 30y2
A) 2y2
B) 2y2u6
C) 6y2u6
D) 6y9u9
E) 6y2
2. Factor out the common factor.
6m(7m + 3) (7m + 3)
A) (7m + 3)6m
B) (7m + 3)6m 1
C) (7m + 3)6m + 1
D) (7m + 3)(6m 1)
E) (
M1111-CH-1
Chapter 1:
Equations, Inequalities, and Math Modeling
1.1: Graphs of Equations
y = 7 3x
A graph of an equation consists of the set of ordered pairs that are solutions
to the equation.
To find intercepts:
x-intercept : set y = 0 and solve for x
Name: _ Date: _
1. Identify the degree and leading coefficient of the polynomial.
7x4y + 7x2y2 + 8xy5
A) degree: 5
B) degree: 6
C) degree: 6
D) degree: 5
E) degree: 4
leading coefficient: 8
leading coefficient: 8
leading coefficient: 7
leading coefficient
Name: _ Date: _
1. Find the standard form of the quadratic function shown below:
A)
B)
C)
D)
E)
2.
Determine the vertex of the graph of the quadratic function f ( x) = x 2 + 5 x +
A)
B)
C)
D)
E)
5 27
,
2 2
29
5,
4
5 29
,
2 4
5 21
,
4