Question 3: Use the function and graph to answer questions about existence, limits, and continuity.

Solution:

• Does f(2) exist?
• Does $\lim_{x \rightarrow 2} f(x)$ exist?
• Does $\lim_{x \rightarrow 2} f(x) = f(2)$
• Is the function continuous at $x=2$?

Question 5: What value should be assigned to f(2) to make the extended function continuous at x = 2?

• Solution:

Question 7: At what points is this function continuous? (describe the set of x-values where the function is continuous, using interval notation)

$$ y= \frac{x+8}{x^2-15x+56} $$

• Solution:

Question 8: Determine the point(s) at which the given function f(x) is continuous. (describe the set of x-values where the function is continuous, using interval notation)

$$ f(x)= |4x-3|+3sin(8x) $$

• Solution: