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In this lesson, we will learn how to find the values of one-sided limits for piecewise-defined functions both graphically and algebraically.

Q1:

Find l i m → 𝑓 ( 𝑥 ) .

Q2:

Determine l i m 𝑥 → − 4 − 𝑓 ( 𝑥 ) , if it exists.

Q3:

Determine 𝑓 ( 0 ) + .

Q4:

Determine l i m 𝑥 → − 6 − 𝑓 ( 𝑥 ) , if it exists.

Q5:

Use the graph below to find l i m 𝑥 → 8 + 𝑓 ( 𝑥 ) .

Q6:

Use the graph below to find l i m 𝑥 → 5 + 𝑓 ( 𝑥 ) .

Q7:

Determine l i m 𝑥 → 0 + 𝑓 ( 𝑥 ) , if it exists.

Q8:

Determine l i m l i m l i m 𝑥 → − 5 𝑥 → − 7 𝑥 → 0 𝑓 ( 𝑥 ) + 𝑓 ( 𝑥 ) + 𝑓 ( 𝑥 ) + − .

Q9:

Determine 𝑓 ( 1 ) − .

Q10:

Determine 𝑓 ( 0 ) − .

Q11:

Using the graph shown, find 𝑓 ( − 3 ) + .

Q12:

Determine l i m 𝑥 → 8 − 𝑓 ( 𝑥 ) .

Q13:

Determine l i m 𝑥 → 1 + 𝑓 ( 𝑥 ) .

Q14:

Determine .

Q15:

Determine l i m 𝑥 → − 3 − 𝑓 ( 𝑥 ) .

Q16:

Determine 𝑓 ( − 3 ) − .

Q17:

Determine l i m 𝑥 → − 6 + 𝑓 ( 𝑥 ) .