Prove that if $f(x)$ is continuous and $K$ is a constant, then $f(x)+K$ is a continuous function.

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Lesson Parent: 
Function Limits VI: Continuous Functions
Problem: 

Prove that if $f(x)$ is continuous and $K$ is a constant, then $f(x)+K$ is a continuous function.

Answer: 

It is true that if $f(x)$ is continuous and $K$ is a constant, then $f(x)+K$ is a continuous function.

SAMPLE SOLUTION

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Solution: 

Since $K$ is a constant we know that

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and by the definition of continuity that

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If we set <Sign in to see all the formulas> then we know that

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Therefore,

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and the function <Sign in to see all the formulas> is continuous.