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Admission in India 2015

By:admission.edhole.com

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Essential Questions

1)What is the difference between an odd and even function?

2)How do you perform transformations on polynomial functions?

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Even and Odd Functions (graphically)

If the graph of a function is symmetric with respect to the y-axis, then it’s even.

If the graph of a function is symmetric with respect to the origin, then it’s odd.

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Even and Odd Functions (algebraically)

A function is even if f(-x) = f(x)

A function is odd if f(-x) = -f(x)

If you plug in -x and get the original function, then it’s even.

If you plug in -x and get the opposite function, then it’s odd.

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Let’s simplify it a little…

We are going to plug in a number to simplify things. We will usually use 1 and -1 to compare, but there is an exception to the rule….we will see soon!

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f x x( ) Even, Odd or Neither?Ex. 1

f x x( ) Graphically Algebraically

(1) 1 1f ( 1) 1 1f

They are the same, so it is.....

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f x x x( ) 3Even, Odd or Neither?

Ex. 2

3( )f x x x Graphically Algebraically

3(2) (2) (2)f 6

63( 2) ( 2) ( 2)f

They are opposite, so…

What happens if we plug in 1?

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f x x( ) 2 1Even, Odd or Neither?

2( ) 1f x x Graphically Algebraically

2(1) (1) 1f

22( 1) ( 1) 1f

Ex. 3

2They are the same, so.....

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3( ) 1f x x Even, Odd or Neither?

3( ) 1f x x Graphically Algebraically

3(1) (1) 1f

0

2

3( 1) ( 1) 1f

They are not = or opposite, so...

Ex. 4

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Let’s go to the Task….

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What happens when What happens when we change the we change the

equations of these equations of these parent functions?parent functions?

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14)9()( 2 xxf

3)2()( xxf

Left 9 , Down 14

Left 2 , Down 3

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-f(x)

f(-x)

Reflection in the x-axis

Reflection in the y-axis

What did the negative on the outside do?

What do you think the negative on the inside will do?

Study tip: If the sign is on the outside it has “x”-scaped

Study tip: If the sign is on the inside, say “y” am I in here?

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Write the Equation to this Graph

2)3( 2 xy

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Write the Equation to this Graph

1)2( 3 xy

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Write the Equation to this Graph

11 xy

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Write the Equation to this Graph

3 3( ) ( ) 2 or ( ) ( ) 2f x x f x x admission.edhole.com

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Example: Sketch the graph of f (x) = – (x + 2)4 .

This is a shift of the graph of y = – x 4 two units to the left.

This, in turn, is the reflection of the graph of y = x 4 in the x-axis.

x

y

y = x4

y = – x4f (x) = – (x + 2)4

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Compare:3 3 31

( ) ( ) 4 ( )4

f x x and g x x and h x x

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Compare…

What does the “a” do?

2 2( ) to ( ) 3f x x f x x

Compare… 2 21( ) to ( )

2f x x f x x

• What does the “a” do?

Vertical stretch

Vertical shrink

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Nonrigid Transformations

h(x) = c f(x) c >1

0 < c < 1

Vertical stretch

Vertical shrink

Closer to y-axis

Closer to x-axis

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Polynomial functions of the form f (x) = x n, n 1 are called

power functions.

If n is even, their graphs resemble the graph of

f (x) = x2.

If n is odd, their graphs resemble the graph of

f (x) = x3.

x

y

x

y

f (x) = x2

f (x) = x5f (x) = x4

f (x) = x3

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