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Question 1 of 4
Identify if the curve f(x)=x2f(x)=x2 is an odd or 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 xx to the function
f(x)f(x) |
== |
x2x2 |
f(-x)f(−x) |
== |
(-x)2(−x)2 |
f(-x)f(−x) |
== |
x2x2 |
f(-x)f(−x) |
== |
f(x)f(x) |
f(x)=x2f(x)=x2 |
Since f(-x)=f(x)f(−x)=f(x), f(x)=x2f(x)=x2 is an even function
An even function is symmetric on the y-axis
Even FunctionEven Function
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Question 2 of 4
Identify if the curve f(x)=x3f(x)=x3 is an odd or 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 xx to the function
f(x)f(x) |
== |
x3x3 |
f(-x)f(−x) |
== |
(-x)3(−x)3 |
f(-x)f(−x) |
== |
-x3−x3 |
f(-x)f(−x) |
== |
-f(x)−f(x) |
-f(x)=-x3−f(x)=−x3 |
Since f(-x)=-f(x)f(−x)=−f(x), f(x)=x3f(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)=x4f(x)=x4 is an odd or 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 xx to the function
f(x)f(x) |
== |
x4x4 |
f(-x)f(−x) |
== |
(-x)4(−x)4 |
f(-x)f(−x) |
== |
x4x4 |
f(-x)f(−x) |
== |
f(x)f(x) |
f(x)=x4f(x)=x4 |
Since f(-x)=f(x)f(−x)=f(x), f(x)=x4f(x)=x4 is an even function
Even FunctionEven Function
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Question 4 of 4
Identify if the curve f(x)=x2+2xf(x)=x2+2x is an odd or 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 xx to the function
f(x)f(x) |
== |
x2+2xx2+2x |
f(-x)f(−x) |
== |
(-x)2+2(-x)(−x)2+2(−x) |
f(-x)f(−x) |
== |
x2-2xx2−2x |
Since the curve does not satisfy both condition, f(x)=x2+2xf(x)=x2+2x is neither odd nor even function