Transcript Lesson 1.1 Essential Ideas

Lesson 1.1
Essential Ideas
 A relation is a set of ordered pairs
mapping between two sets, the
domain and range.
 The domain of a relation/function is
the set of all possible input values.
 The range of a relation/function is the
set of all possible output values.
 A function is a relation that maps
each member of the domain onto one
and only one member of the range.
 Verbal descriptions, tables, diagrams,
algebraic symbols, and graphs are
used to represent relations and
functions.
Lesson 1.2
Essential Ideas
 The graph of a linear function is a line.
 The slope of a linear function is the unit
rate of change and is constant.
 The absolute value of a number is the
distance from the number to zero on the
number line.
 The graph of an absolute value function is
v-shaped, composed of two rays
 An absolute value function has an extreme
point (extrema) which is a minimum or
maximum point, called a vertex.
 When a line can be drawn on a graph that
divides the graph into two mirror images,
the graph has line symmetry. This line is
called the line of symmetry.
 The graph of an absolute function has a
line of symmetry drawn through the vertex.
Lesson 1.3
Essential Ideas
 Graphical representations provide us with
information about the relationship between the
independent and dependent variables, including
increase, decrease, and no change.
 An interval of increase is a set of values of x with
no gaps for which y is increasing. An interval of
decrease is a set of values of x with no gaps for
which y is decreasing.
 A quadratic function is a function with an
algebraic equation featuring an independent
variable with an exponent of 2.
 The graph of a quadratic function is U-shaped.
 The domain of a quadratic function is all
numbers.
 The range of a quadratic function is all numbers
greater than or equal to the y- value of the
vertex, if the leading coefficient is positive, or all
numbers less than or equal to the y-value of the
vertex, if the leading coefficient is negative.
 The vertex of a quadratic function is the
extreme point on the graph of the
quadratic function.
 The line of symmetry is the vertical line
drawn through the vertex, with an equation
of x = (the x-value of the vertex).
Lesson 1.4
Essential Ideas
 A Cubic Function is a third-degree function
 An Indirect Variation Function is of the
form y=k/x.
 In an indirect function, the values of the
variables increase and decrease
proportionally in opposite directions.
Lesson 1.5
Essential Ideas
 A Square Root Function is a function in
which the independent variable is under a
radical symbol.
 An Exponential Function is a function in
which the independent variable is an
exponent.
 The Average Rate of Change between two
points on the graph of a function is the
change in y divided by the change in x.