1. Keeper 8 Honors Calculus
Graphs From Limits
Keeper 8
Honors Calculus

2. Drawing A Graph From Limits
Draw in any point value 𝑓 =#
Draw in any asymptotes
Vertical: lim 𝑥→# 𝑓 𝑥 =±∞
Horizontal: lim 𝑥→±∞ 𝑓(𝑥) =#
Draw arrows
Connect
*** Be sure that the graph drawn is a function! It must pass the vertical line test!!!

3. Example 1 – Create the Graph Given the Limits
Given: lim 𝑥→∞ 𝑓(𝑥) =2 lim 𝑥→1 𝑓(𝑥) =−2 lim 𝑥→−∞ 𝑓(𝑥) =2 𝑓 1 =2

4. Example 2 – Create the Graph Given the Limits
Given: lim 𝑥→∞ 𝑓(𝑥) = 0 lim 𝑥→ −2 + 𝑓(𝑥) =∞ lim 𝑥→ −2 − 𝑓(𝑥) =∞ lim 𝑥→−∞ 𝑓(𝑥) =0 𝑓 −2 =−3

5. Example 3 – Create the Graph Given the Limits
Given: lim 𝑥→∞ 𝑓(𝑥) =∞ lim 𝑥→ 0 + 𝑓(𝑥) =∞ lim 𝑥→ 0 − 𝑓(𝑥) =−∞ lim 𝑥→−∞ 𝑓(𝑥) =1

6. Example 4 – Create the Graph Given the Limits
Given: lim 𝑥→∞ 𝑓(𝑥) =3 lim 𝑥→ 2 + 𝑓(𝑥) =∞ lim 𝑥→ 2 − 𝑓(𝑥) =0 lim 𝑥→−∞ 𝑓(𝑥) =−∞

7. Example 5 – Create the Graph Given the Limits
Given: lim 𝑥→∞ 𝑓(𝑥) =−∞ lim 𝑥→ 1 + 𝑓(𝑥) =∞ lim 𝑥→ 1 − 𝑓(𝑥) =−∞ lim 𝑥→−∞ 𝑓(𝑥) =∞

8. Example 6 – Create the Graph Given the Limits
Given: lim 𝑥→∞ 𝑓(𝑥) =2 lim 𝑥→−2 𝑓(𝑥) =−4 lim 𝑥→ 1 + 𝑓(𝑥) =−2 lim 𝑥→ 1 − 𝑓(𝑥) =−∞ lim 𝑥→−∞ 𝑓(𝑥) =−∞ 𝑓 −2 =3 𝑓 1 =4