200 300 100 300 100 200 300 100 200 300 100 200 300 100 domains & ranges i love parametric...
TRANSCRIPT
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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
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| 5
| 0
D x x
R y y
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Find the domain of the following equation in
interval notation:
3xy
x
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[ 3,0) (0, )D
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Find the domain of the following equation:
2 5 6y x x
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| ( 2) ( 3)D x x x
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Parameterize this equation:
3 5 6y x x
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3
( )
( ) 5 6
x t t
y t t t
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Find the inverse of this parametric equation:
2
( ) 3 1
( ) 4
x t t
y t t t
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2( ) 4
( ) 3 1
x t t t
y t t
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Graph the inverse of this parametric equation:
2
( ) 2 1
( )
1 1
x t t
y t t t
t
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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))
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xx22 + 2x + 2x
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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)
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2x2x22 + 3x - 5 + 3x - 5
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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)))
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8x + 38x + 3
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Find the inverse of the equation:
3 15y x
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53
xy
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Find the inverse of the equation:
2 4y x x
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4 2x y
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Find the inverse of the equation:
2122 2 xxy
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32
16
x
y
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Find the difference quotient of the function
f(x) = 3x - 5
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3
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Find the difference quotient of the function
f(x) = 3x2 – x + 1
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6x + 3h -1
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Find the slope of the secant line of the function
f(x) = x2 – 2x + 1
for the interval
[-1, 2]
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-1
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List the symmetries of List the symmetries of the equation y = 2xthe equation y = 2x
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symmetric about the symmetric about the originorigin
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List the symmetries of the List the symmetries of the equation yequation y22 = x - 3 = x - 3
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symmetric about the symmetric about the x-axisx-axis
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List the symmetries of List the symmetries of the equation the equation
y = |x| + xy = |x| + x22
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symmetric about the symmetric about the y-axisy-axis
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Is the function in the graph even, odd, or neither?
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NEITHER
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Is the function in the graph even, odd, or neither?
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ODD
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List the symmetries of even functions and list the
symmetries of odd functions.
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Even – symmetric about y-axisOdd – Symmetric about origin