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200 300 100 300 100 200 300 100 200 300 100 200 300 100 Domains & Ranges I LOVE Parametric Equations...
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Transcript of 200 300 100 300 100 200 300 100 200 300 100 200 300 100 Domains & Ranges I LOVE Parametric Equations...
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Domains &Ranges
I LOVE ParametricEquations
Operationsof
Functions
Inverse Functions
Difference Quotient
Symmetry
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Odds and Evens
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Find the domain and the range of the following
equation:
1
5y
x
| 5
| 0
D x x
R y y
Find the domain of the following equation in
interval notation:
3xy
x
[ 3,0) (0, )D
Find the domain of the following equation:
2 5 6y x x
| ( 2) ( 3)D x x x
Parameterize this equation:
3 5 6y x x
3
( )
( ) 5 6
x t t
y t t t
Find the inverse of this parametric equation:
2
( ) 3 1
( ) 4
x t t
y t t t
2( ) 4
( ) 3 1
x t t t
y t t
Graph the inverse of this parametric equation:
2
( ) 2 1
( )
1 1
x t t
y t t t
t
Given the following functions:Given the following functions:
f(x) = x + 1f(x) = x + 1
h(x) = xh(x) = x22 - 1 - 1
Find h(f(x))Find h(f(x))
xx22 + 2x + 2x
Given the following functions:Given the following functions:
f(x) = 2x + 5f(x) = 2x + 5
g(x) = x - 1g(x) = x - 1
Find f(x)*g(x)Find f(x)*g(x)
2x2x22 + 3x - 5 + 3x - 5
Given the following functions:Given the following functions:
f(x) = 2x + 5f(x) = 2x + 5
g(x) = x – 1g(x) = x – 1
h(x) = 4xh(x) = 4x
Find f(g(h(x)))Find f(g(h(x)))
8x + 38x + 3
Find the inverse of the equation:
3 15y x
53
xy
Find the inverse of the equation:
2 4y x x
4 2x y
Find the inverse of the equation:
2122 2 xxy
32
16
x
y
Find the difference quotient of the function
f(x) = 3x - 5
3
Find the difference quotient of the function
f(x) = 3x2 – x + 1
6x + 3h -1
Find the slope of the secant line of the function
f(x) = x2 – 2x + 1
for the interval
[-1, 2]
-1
List the symmetries of List the symmetries of the equation y = 2xthe equation y = 2x
symmetric about the symmetric about the originorigin
List the symmetries of the List the symmetries of the equation yequation y22 = x - 3 = x - 3
symmetric about the symmetric about the x-axisx-axis
List the symmetries of List the symmetries of the equation the equation
y = |x| + xy = |x| + x22
symmetric about the symmetric about the y-axisy-axis
Is the function in the graph even, odd, or neither?
NEITHER
Is the function in the graph even, odd, or neither?
ODD
List the symmetries of even functions and list the
symmetries of odd functions.
Even – symmetric about y-axisOdd – Symmetric about origin