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

Date post: 03-Jan-2016
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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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Page 1: 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.

200

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Domains &Ranges

I LOVE ParametricEquations

Operationsof

Functions

Inverse Functions

Difference Quotient

Symmetry

100

200

300

Odds and Evens

100

200

300

200

Page 2: 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.

Find the domain and the range of the following

equation:

1

5y

x

Page 3: 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.

| 5

| 0

D x x

R y y

Page 4: 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.

Find the domain of the following equation in

interval notation:

3xy

x

Page 5: 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.

[ 3,0) (0, )D

Page 6: 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.

Find the domain of the following equation:

2 5 6y x x

Page 7: 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.

| ( 2) ( 3)D x x x

Page 8: 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.

Parameterize this equation:

3 5 6y x x

Page 9: 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.

3

( )

( ) 5 6

x t t

y t t t

Page 10: 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.

Find the inverse of this parametric equation:

2

( ) 3 1

( ) 4

x t t

y t t t

Page 11: 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.

2( ) 4

( ) 3 1

x t t t

y t t

Page 12: 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.

Graph the inverse of this parametric equation:

2

( ) 2 1

( )

1 1

x t t

y t t t

t

Page 13: 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.

 

Page 14: 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.

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))

Page 15: 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.

xx22 + 2x + 2x

Page 16: 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.

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)

Page 17: 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.

2x2x22 + 3x - 5 + 3x - 5

Page 18: 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.

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)))

Page 19: 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.

8x + 38x + 3

Page 20: 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.

Find the inverse of the equation:

3 15y x

Page 21: 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.

53

xy

Page 22: 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.

Find the inverse of the equation:

2 4y x x

Page 23: 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.

4 2x y

Page 24: 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.

Find the inverse of the equation:

2122 2 xxy

Page 25: 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.

32

16

x

y

Page 26: 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.

Find the difference quotient of the function

f(x) = 3x - 5

Page 27: 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.

3

Page 28: 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.

Find the difference quotient of the function

f(x) = 3x2 – x + 1

Page 29: 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.

6x + 3h -1

Page 30: 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.

Find the slope of the secant line of the function

f(x) = x2 – 2x + 1

for the interval

[-1, 2]

Page 31: 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.

-1

Page 32: 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.

List the symmetries of List the symmetries of the equation y = 2xthe equation y = 2x

Page 33: 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.

symmetric about the symmetric about the originorigin

Page 34: 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.

List the symmetries of the List the symmetries of the equation yequation y22 = x - 3 = x - 3

Page 35: 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.

symmetric about the symmetric about the x-axisx-axis

Page 36: 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.

List the symmetries of List the symmetries of the equation the equation

y = |x| + xy = |x| + x22

Page 37: 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.

symmetric about the symmetric about the y-axisy-axis

Page 38: 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.

Is the function in the graph even, odd, or neither?

Page 39: 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.

NEITHER

Page 40: 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.

Is the function in the graph even, odd, or neither?

Page 41: 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.

ODD

Page 42: 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.

List the symmetries of even functions and list the

symmetries of odd functions.

Page 43: 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.

Even – symmetric about y-axisOdd – Symmetric about origin


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