Term 1 Long Test 1 – Coverage
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Concepts to Master
Relations and Functions
Domain and Range
Different ways of Representing Relations and Functions
(Descriptive rule, Mapping Diagram, Table, Ordered Pairs, Equations & Graphs)
Function Notation, f(x)
Zeros of Functions
Quadratic Functions, 𝑓(𝑥) = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐, where 𝑎, 𝑏 and 𝑐 are constants such that 𝑎 ≠ 0
Linear Functions, 𝑓(𝑥) = 𝑚𝑥 + 𝑏, where 𝑚 and 𝑏 are constants such that 𝑚 ≠ 0
Constant Functions, 𝑓(𝑥) = 𝑏 where 𝑏 is a constant such that 𝑏 ≠ 0
The Zero Function, 𝑓(𝑥) = 0
Characteristics of the three functions above. (See table in succeeding pages.)
Skills to Review and Master
Prerequisite Skills
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Factoring (See website for exercises.)
CTS
Solving Systems of Equations (p 81-82)
Operations on Radicals and Simplifying Radicals (See website for exercises.)
Operations on Fractions and Simplifying Fractions
Current
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Identifying if a relation (in any representation) is a function and not a mere relation:
Graphs – use vertical line test
Set of Ordered Pairs - no repetition of the x-coordinate
Mapping Diagram – 1-1 and m-1
Rule, Table and Equations – convert to any of the three above and then use the indicated test
Evaluating Functions (in any representation)
Converting form general to vertex form and vice versa
Vertex to General Form – expand the square of the binomial
General to Vertex Form-– use CTS
Graphing of Lines and Parabolas
Finding Equations of Lines or Parabolas
Simplifying non-real numbers in terms of 𝑖
Solving QE 1V – Factoring, CTS, Quadratic Formula
Solving Equations that are Quadratic in Form
Solving QI 1V - TOS, Graphical, by Inspection
Solving Intercepts
Solving for the zeros
Identifying Characteristics of The Zero, Constants, Linear and Quadratic Functions
Working with general constants (a, b, c, h and k)
Characteristics
The Zero
Function
Constant
Functions
Linear Functions
Quadratic Functions
Form of Equation
𝑓(𝑥) = 0
𝑓(𝑥) = 𝑏 where
b is a constant
such that 𝑏 ≠ 0
𝑓(𝑥) = 𝑚𝑥 + 𝑏, where
𝑚 and 𝑏 are constants
such that 𝑚 ≠ 0
General Form:
𝑓(𝑥) = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐,
where 𝑎, 𝑏 and 𝑐 are
constants such that 𝑎 ≠ 0
Vertex Form:
𝑓(𝑥) = 𝑎(𝑥 − ℎ)2 + 𝑘
where a, h and k are
constants such that 𝑎 ≠ 0
Slope
0
0
𝑚
has no slope since it is not a
line
(Slopes of parallel lines
are equal.
Slopes of perpendicular
are negative reciprocal of
each other)
Vertex
has no vertex
has no vertex
(ℎ, 𝑘)
has no vertex
ℎ=−
𝑏
, 𝑘 = 𝑓(ℎ)
2𝑎
Axis of Symmetry
y-axis
y-axis
perpendicular line to the
graph
𝑥=ℎ
Domain
R
R
R
R
{0}
{𝑏}
R
𝑎 > 0 - opening up:
(set of all
permissible values
of x)
Range
(set of all
resulting 𝒚 values)
{𝑓(𝑥)|𝑓(𝑥) ≥ 𝑘}
𝑎 < 0 - opening down:
{𝑓(𝑥)|𝑓(𝑥) ≥ 𝑘}
𝒚-intercept
(value of 𝒚 when
𝒙 is zero)
0
𝑏
𝑏
𝑐
𝒙-intercept/s
all real
numbers
None
−𝑚
𝑏
(real number
value of 𝒙 when
𝒚 = 𝒇(𝒙) is zero)
𝑥=
−𝑏 ± √𝑏 2 − 4𝑎𝑐
2𝑎
(if these are real numbers)
Discriminant : 𝒃𝟐 − 𝟒𝒂𝒄
Positive : 2 𝑥-intercepts
Zero : 1 𝑥-intercept
Negative: no 𝑥-intercept
Zero/s
all real
numbers
None
(value/s of 𝒙 (real
on not-real) such
that 𝒚 = 𝒇(𝒙) is
zero)
−𝑚
𝑏
(same as the 𝑥-intercept)
𝑥=
−𝑏 ± √𝑏 2 − 4𝑎𝑐
2𝑎
Can be real or non-real;
Not always the same as the
𝑥-intercept
Discriminant : 𝒃𝟐 − 𝟒𝒂𝒄
Positive : 2 real and
different from each other
(distinct)
Zero: 2 real and same (nondistinct); a zero of
multiplicity 2
Negative: 2 non-real and
different from each other
(distinct)
Graph
Horizontal
Line on the 𝑥axis
Horizontal line
with 𝑦-intercept
𝑏
Diagonal line with slope 𝑚
and 𝑦-intercept 𝑏
Parabola
Behavior
neither
neither
𝑚 > 0 – increasing
𝑚 < 0 – decreasing
Both Decreasing and
Increasing
Depends on the opening
and the vertex