MAT 145 Quiz  #3   Name  __________________________    10  points   Calculator  Used  _____________________________    Impact  on  Course  Grade:  approximately  1%-­‐2%   Section  _____________________________    1–8)  1  pt  each;  (9)  2  pts   Show  evidence  to  support  your  solutions!        Score     _________________________  

Review your responses. Do they seem reasonable for each situation?

The graph of function y = f(x) is shown here. Use it to determine responses for (1) through (6).

1)      lim!→!

𝑓(𝑥)  ___________

2) lim!→!!!

𝑓 𝑥  __________

3)   lim!→!!

𝑓 𝑥 ___________

4)   lim!→!

𝑓(𝑥)  ___________

5) 𝑓 −2    _____________ 6) Jan claims that both a vertical asymptote and a horizontal asymptote exist here. Write a complete, accurate, and precise limit statement to support each of Jan’s claims. (a) limit statement (vertical asymptote): ______________ (b) limit statement (horizontal asymptote): ______________

Here is information about limits of functions y = g(x) and y = h(x). Use this information and your knowledge of limits to simplify the limit expression stated in question (7). For (8) and (9), show labeled algebra steps as you simplify each limit as completely as possible.

lim!→!

𝑔 𝑥 = 2 lim!→!

ℎ 𝑥 = −3 lim!→!!

𝑔 𝑥 = 0 lim!→!!

ℎ 𝑥 = −4

7) lim

!→!!2𝑔 𝑥 − ℎ(𝑥) __________

8)   lim!→!

𝑥! − 3𝑥 − 4 __________

9) lim!→!!

 𝑥! − 𝑥 − 6𝑥 + 2

__________

–7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7