Odd and Even Functions 1
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Question 1 of 4
1. Question
Identify if the curve `f(x)=x^2` is an odd or even functionHint
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Great Work!
Incorrect
Even Functions
`f(-x)=f(x)`Odd Functions
`f(-x)=-f(x)`Substitute negative `x` to the function`f(x)` `=` `x^2` `f(-x)` `=` `(-x)^2` `f(-x)` `=` `x^2` `f(-x)` `=` `f(x)` `f(x)=x^2` Since `f(-x)=f(x)`, `f(x)=x^2` is an even functionAn even function is symmetric on the y-axis
`\text(Even Function)` -
Question 2 of 4
2. Question
Identify if the curve `f(x)=x^3` is an odd or even functionHint
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Correct!
Incorrect
Even Functions
`f(-x)=f(x)`Odd Functions
`f(-x)=-f(x)`Substitute negative `x` to the function`f(x)` `=` `x^3` `f(-x)` `=` `(-x)^3` `f(-x)` `=` `-x^3` `f(-x)` `=` `-f(x)` `-f(x)=-x^3` Since `f(-x)=-f(x)`, `f(x)=x^3` is an odd functionAn odd function is symmetric on the origin
`\text(Odd Function)` -
Question 3 of 4
3. Question
Identify if the curve `f(x)=x^4` is an odd or even functionHint
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Keep Going!
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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^4` `f(-x)` `=` `(-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 functionHint
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Fantastic!
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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)`