Limits and Continuity

What is the average rate of change of the function $f(x) = x^2$ over the interval $[1, 3]$?

Based on the graph of $f(x)$, as $x$ approaches 2, the y-value approaches 5. Which of the following is the correct limit notation?

Given the limit notation $\lim_{x \to a} f(x) = L$, which of the following statements best describes its meaning?

Consider the piecewise function: $$f(x) = \begin{cases} x + 1, & x < 1 \\ x^2 + k, & x \geq 1 \end{cases}$$For what value of $k$ does $\lim_{x \to 1} f(x)$ exist?

From the graph of a function, it is observed that as $x$ approaches 3 from the left, $f(x)$ approaches 2. Which of the following is the correct notation for this observation?

A graph shows that as $x$ approaches 4 from the left, $f(x)$ approaches 7, and as $x$ approaches 4 from the right, $f(x)$ approaches 7. Which of the following statements is true?

Consider a function whose graph oscillates rapidly near $x = 5$. Which of the following is most likely to be true?

Given the following table of values for a function $f(x)$, what is the estimated value of $\lim_{x \to 2} f(x)$?

Given the following table of values, does $\lim_{x \to 3} f(x)$ exist?

Given that $\lim_{x \to 2} f(x) = 4$ and $\lim_{x \to 2} g(x) = 5$, what is the value of $\lim_{x \to 2} [2f(x) + g(x)]$?