200 300 100 300 100 200 300 100 200 300 100 200 300 100 Domains & Ranges I LOVE Parametric Equations...

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200 300 100 300 100 200 300 100 200 300 100 200 300 100 Domains & Ranges I LOVE Parametric Equations Operations of Functions Inverse Functions Difference Quotient Symmetry 100 200 300 Odds and Evens 100 200 300 200

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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

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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


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