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Question 1 of 4
Identify if the curve f(x)=x2 is an odd or even 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) |
= |
x2 |
| f(-x) |
= |
(-x)2 |
| f(-x) |
= |
x2 |
| f(-x) |
= |
f(x) |
f(x)=x2 |
Since f(-x)=f(x), f(x)=x2 is an even function
An even function is symmetric on the y-axis
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Question 2 of 4
Identify if the curve f(x)=x3 is an odd or even 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) |
= |
x3 |
| f(-x) |
= |
(-x)3 |
| f(-x) |
= |
-x3 |
| f(-x) |
= |
-f(x) |
-f(x)=-x3 |
Since f(-x)=-f(x), f(x)=x3 is an odd function
An odd function is symmetric on the origin
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Question 3 of 4
Identify if the curve f(x)=x4 is an odd or even 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) |
= |
x4 |
| f(-x) |
= |
(-x)4 |
| f(-x) |
= |
x4 |
| f(-x) |
= |
f(x) |
f(x)=x4 |
Since f(-x)=f(x), f(x)=x4 is an even function
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Question 4 of 4
Identify if the curve f(x)=x2+2x is an odd or even 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) |
= |
x2+2x |
| f(-x) |
= |
(-x)2+2(-x) |
| f(-x) |
= |
x2-2x |
Since the curve does not satisfy both condition, f(x)=x2+2x is neither odd nor even function
