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Parent Functions For Dummies

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by

Victor Arahirwa

on 19 March 2014

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Transcript of Parent Functions For Dummies

Linear Function: f(x)=x
Constant Function: f(x) = c
Absolute value function: f(x)=|x|
Square Root Parent Function: f(x) = √x
Quadratic Parent Function: f(x) = x^2
Graph:
Rational Parent Function: f(x)=1/x
Graph:
Graph:
Graph:
Graph:
Parent Functions For Dummies
Domain
The set of all possible x-values
Make the function "work", and will output real y-values.
Range
The set of all possible y-values
Depends on the input (domain)
Domains and Ranges
Domain: (-∞,∞)
Range: constant
y-intercept: y=c
x-intercept: none
Constant through (-∞,∞)
Even function
Symmetrical to y-axis
No asymptotes
Domain: (-∞,∞)
Range: (-∞,∞)
Y-intercept: y=0
X-intercept: x = 0
Increasing through (-∞,∞)
Odd function
Symmetrical to the origin
No asymptotes
Domain: (-∞,∞)
Range: [0,∞)
x-intercept: x=0
y-intercept: y=0
Decreasing from (-∞,0)
Increasing from (0,∞)
Even function
Symmetrical to y-axis
Asymptotes: none


Domain: [0,∞)
Range: [0,∞)
X-Intercept: X=0
Y-Intercept: Y=0
Increasing through [0,∞)
Neither even nor odd
No symmetry
No Asymptotes
Graph:
Domain: (-∞,0)U(0,∞)
Range:(-∞,0)U(0,∞)
No intercepts
Odd Function
Symmetrical to the Origin
Vertical Asymptotes: x=0
Horizontal Asymptotes: y=0
Decreasing: (-∞,0)U(0,∞)
Cubic Parent Function: F(x)=x^3
Graph:
Domain: (-∞,∞)
Range: [0,∞)
X-intercept: x=0
Y-intercept: y=0
Decreasing through (-∞,0)
Increasing through (0,∞)
Even function
Symmetrical to y-axis
No asymptotes
Domain: (-∞,∞)
Range: [0,∞)
X-intercept: x=0
Y-intercept: y=0
Increasing through (-∞,∞)
Odd Function
Symmetrical to the origin
No asymptotes
Greatest Integer Parent Function f(x)=[[x]]
How can you tell if a function is even or odd?
Graph:
Domain: All Real Numbers
Range: All Integers
X-intercept: x=[0,1)
Y-intercept: y= 0
Constant within each interval
Neither even nor odd
No symmetry
No asymptotes
If f(-x) = f(x) the function is even
If f(-x) = -f(x) the function is odd
Pablo Is Awesome!!!!
The points where the graph touches either the x-axis or y-axis
Make y=0 or x=0 and see the value of x or y at these points
What are asymptotes?
They are lines that the graph approaches as it gets closer to infinity.
They limit the domain/range of a function.
What are intercepts?
Exponential Growth Parent Function: f(x) = ab^(x-h) + k
Graph:
Domain: (-∞,∞)
Range: (k,∞) or (k,-∞)

Asymptote: y=k
Y-intercept:
y = a when h=0 & k=0
make x=o and solve for y when h & k are not 0
X-intercept: none
Increasing through (-∞,∞)
Neither even nor odd
No symmetry

Finding domain and range
Did you know?
In a function for every input there is exactly one output
Functions can be represented verbally, numerically, graphically, and algebraically.
Parent functions have a lot of children.
Increasing, decreasing, and constant intervals are related to the
monotone
of a function.
Functions can transform across the x-axis, up or down the y-axis.

If the graph is symmetrical to the y-axis, the function is even.
If the graph is symmetrical to the origin, the function is odd.
Transformations
There are two types of transformations:
Rigid
Horizontal shifts
Vertical shifts
Reflections: h(x) = -f(x), h(x) = f(-x)
Nonrigid
Change in shape
Stretches and shrinks

Vertical & Horizontal Shifts
c is positive real number
Vertical and horizontal shift in the graph of y=f(x)
Vertical shift
Upward: h(x)=f(x)+c
Downward: h(x)=f(x)-c
Horizontal shift
Right h(x)=f(x-c)
Left h(x)=f(x+c)
Tiffany Rocks!!!
Vertical and Horizontal Stretches and Shrinks
g(x) = cf(x)
if c > 1, vertical stretch
if 0 < c <1, vertical shrink
h(x) = f(cx)
if c >1, horizontal shrink
if 0 < c < 1, horizontal stretch
Full transcript