y=|x|
y=1/x
y= sqrt{x}
y=x
y=x^2
Step Pattern:
Over 1, up 1
Over 1, up 3
Over 1, up 5
Step Pattern:
Up 1, over 1
Up 1, over 3
Up 1, over 5
Step Pattern:
Up 1, over 1
Up 1, over 1
Up 1, over 1
Unit 2-Functions
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6) Translations of
Parent Functions
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Writing the Equation
example. (absolute value function)
Horizontal
In this graph, only x changes, but y remains the same
Vertical
-only the y changes, x stays the same
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1) Relations and Functions
Function
Day, Date,Hour
-used to find out whether graph is a function
-Using a ruler, place it vertically on the graph
-Start from one end of graph and bring ruler
across it, keeping it in the same upwards position
-If two points shown on same vertical line, it's not
a function
Vertical Line Test
A function is a set of inputs, in relation
to a set of outputs. Each input has its own
output. For every x-value, there is one
y-value.
Relation
A relation is a set of ordered pairs
ex, (x,y)
Set Notation
A set is a collection of values/items
which are listed inside curly brackets.
This is a set notation, the domain
and range are also stated.
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2) Function Notation
and evaluating functions
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The label 'fx' is used
to represent the y-value/dependent
variable of a function. It is the
output of a function.
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In both a) and b), you must plug in the numbers accordingly. In a), the '+5' goes after the function, however
for b) the '2' goes in front of the function.
Placing the given numbers in the incorrect
spot can change the equation.
Determining the
value of a function
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5) The Inverse of a Function
& its Properties
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Quadratic Function:
inverse does not pass vertical
line test, therefore it's not a
function
Inverse: Linear
Given this equation find the inverse
Using the vertical line method,
the inverse is proven to be a function
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Equation
Inverse Function is when
two functions are
the reverse of each other
or the opposite of one
another.
How to find inverse?
Switch x and y
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-if equation is given
-same rule applies, switch
x and y
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-If set of points are given
-Switch x and y values
Name the author.
3) Domain and Range
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Range
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Range is the set
of values for the y-variable.
(dependent variable)
Diagram
Domain
Select as needed:
Domain is the set of
values for the x-values.
(independent variable)
4) Parent Functions
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Course objectives
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Absolute Value
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Reciprocal Function
Quadratic/Parabola
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Square Root Function
Linear Function
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What is it?
A parent function is the simplest function
in a family of functions
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The Different Types:
-Linear
-Square Root
-Quadratic
-Reciprocal
-Absolute Value
