In this lesson, we will learn how to differentiate between the three types of function discontinuity at a given point.
Students will be able to
Q1:
Consider the function 𝑓(𝑥)=1−𝑥𝑥<0,0𝑥=0,1+2𝑥𝑥>0.whenwhenwhen
What is 𝑓(0)?
What is lim→𝑓(𝑥)?
What is lim→𝑓(𝑥)?
What type of discontinuity does the function 𝑓 have at 𝑥=0?
Q2:
Consider the function 𝑓(𝑥)=⎧⎪⎨⎪⎩1𝑥,𝑥<0,0,𝑥=0,1𝑥,𝑥>0.sinwhenwhenwhen
Q3:
Consider the function 𝑓(𝑥)=𝑥−9𝑥−3.
Find the type of discontinuity that the function 𝑓 has at 𝑥=3, if it has any.
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