Odd and Even Functions 1

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Question 1 of 4

1. Question
Identify if the curve $f (x) = x^{2}$ $f(x)=x^2$ is an odd or even function
- 1. $Even Function$ $\text(Even Function)$
- 2. $Odd Function$ $\text(Odd Function)$
- 3. $Neither$ $\text(Neither)$
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Even Functions

$f (- x) = f (x)$ $f(-x)=f(x)$

Odd Functions

$f (- x) = - f (x)$ $f(-x)=-f(x)$

Substitute negative $x$ $x$ to the function

$f (x)$ $f(x)$ $=$ $=$ $x^{2}$ $x^2$

$f (- x)$ $f(-x)$ $=$ $=$ ${(- x)}^{2}$ $(-x)^2$

$f (- x)$ $f(-x)$ $=$ $=$ $x^{2}$ $x^2$

$f (- x)$ $f(-x)$ $=$ $=$ $f (x)$ $f(x)$ $f (x) = x^{2}$ $f(x)=x^2$

Since $f (- x) = f (x)$ $f(-x)=f(x)$ , $f (x) = x^{2}$ $f(x)=x^2$ is an even function

An even function is symmetric on the y-axis

$Even Function$ $\text(Even Function)$
Question 2 of 4

2. Question
Identify if the curve $f (x) = x^{3}$ $f(x)=x^3$ is an odd or even function
- 1. $Odd Function$ $\text(Odd Function)$
- 2. $Even Function$ $\text(Even Function)$
- 3. $Neither$ $\text(Neither)$
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Even Functions

$f (- x) = f (x)$ $f(-x)=f(x)$

Odd Functions

$f (- x) = - f (x)$ $f(-x)=-f(x)$

Substitute negative $x$ $x$ to the function

$f (x)$ $f(x)$ $=$ $=$ $x^{3}$ $x^3$

$f (- x)$ $f(-x)$ $=$ $=$ ${(- x)}^{3}$ $(-x)^3$

$f (- x)$ $f(-x)$ $=$ $=$ $- x^{3}$ $-x^3$

$f (- x)$ $f(-x)$ $=$ $=$ $- f (x)$ $-f(x)$ $- f (x) = - x^{3}$ $-f(x)=-x^3$

Since $f (- x) = - f (x)$ $f(-x)=-f(x)$ , $f (x) = x^{3}$ $f(x)=x^3$ is an odd function

An odd function is symmetric on the origin

$Odd Function$ $\text(Odd Function)$
Question 3 of 4

3. Question
Identify if the curve $f (x) = x^{4}$ $f(x)=x^4$ is an odd or even function
- 1. $Neither$ $\text(Neither)$
- 2. $Odd Function$ $\text(Odd Function)$
- 3. $Even Function$ $\text(Even Function)$
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Even Functions

$f (- x) = f (x)$ $f(-x)=f(x)$

Odd Functions

$f (- x) = - f (x)$ $f(-x)=-f(x)$

Substitute negative $x$ $x$ to the function

$f (x)$ $f(x)$ $=$ $=$ $x^{4}$ $x^4$

$f (- x)$ $f(-x)$ $=$ $=$ ${(- x)}^{4}$ $(-x)^4$

$f(-x)$ $=$ $x^4$

$f(-x)$ $=$ $f(x)$ $f(x)=x^4$

Since $f(-x)=f(x)$ , $f(x)=x^4$ is an even function

$\text(Even Function)$
Question 4 of 4

4. Question
Identify if the curve $f(x)=x^2+2x$ is an odd or even function
- 1. $\text(Neither)$
- 2. $\text(Even Function)$
- 3. $\text(Odd Function)$
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Even Functions

$f(-x)=f(x)$

Odd Functions

$f(-x)=-f(x)$

Substitute negative $x$ to the function

$f(x)$ $=$ $x^2+2x$

$f(-x)$ $=$ $(-x)^2+2(-x)$

$f(-x)$ $=$ $x^2-2x$

Since the curve does not satisfy both condition, $f(x)=x^2+2x$ is neither odd nor even function

$\text(Neither)$

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Quiz summary

Information

1. Question

Hint

Great Work!

Even Functions

Odd Functions

2. Question

Hint

Correct!

Even Functions

Odd Functions

3. Question

Hint

Keep Going!

Even Functions

Odd Functions

4. Question

Hint

Fantastic!

Even Functions

Odd Functions

Quizzes

$f (x)$ $f(x)$	$=$ $=$	$x^{2}$ $x^2$
$f (- x)$ $f(-x)$	$=$ $=$	${(- x)}^{2}$ $(-x)^2$
$f (- x)$ $f(-x)$	$=$ $=$	$x^{2}$ $x^2$
$f (- x)$ $f(-x)$	$=$ $=$	$f (x)$ $f(x)$	$f (x) = x^{2}$ $f(x)=x^2$

$f (x)$ $f(x)$	$=$ $=$	$x^{3}$ $x^3$
$f (- x)$ $f(-x)$	$=$ $=$	${(- x)}^{3}$ $(-x)^3$
$f (- x)$ $f(-x)$	$=$ $=$	$- x^{3}$ $-x^3$
$f (- x)$ $f(-x)$	$=$ $=$	$- f (x)$ $-f(x)$	$- f (x) = - x^{3}$ $-f(x)=-x^3$

$f (x)$ $f(x)$	$=$ $=$	$x^{4}$ $x^4$
$f (- x)$ $f(-x)$	$=$ $=$	${(- x)}^{4}$ $(-x)^4$
$f(-x)$	$=$	$x^4$
$f(-x)$	$=$	$f(x)$	$f(x)=x^4$