Pre-Video Questions

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Before watching the videos, think about and answer these questions to the best of your ability.

Below is the graph of $y = f(x)$ .

Which statement about $f(x)$ is true?

(a) $f(2)$ is defined (b) $\lim \limits _{x \to 2} f(x)$ exists (c) $\lim \limits _{x \to 2} f(x) = f(2)$ Both (a) and (b) are true. (a), (b), and (c) are true.

Consider the piecewise function defined by

$f(x) = \begin {cases} x^2-a & \textrm {for } x< 5 \\ 3x+2 & \textrm {for } x \geq 5 \end {cases}$ Which value for $a$ makes the function $f$ continuous?

-2 5 8 17 25

Below is the graph of $f(x) = \dfrac {x^3-x^2-3x+3}{x-1}$ .

Which statement about is true?

(a) $f(1)$ is defined (b) $\lim \limits _{x\to 1} f(x)$ exists (c) $\lim \limits _{x \to 1} f(x) = f(4)$ Both (a) and (b) are true. (a), (b), and (c) are true.

Below is the graph of $f(x) = \dfrac {-x^2+5x-4}{x-4}$ .

Is $f$ continuous for all values of $x$ ?

Yes No I need more information to answer the question.

Overall, how confident are you in your answers?

Not at all confident Not very confident Somewhat confident Very Confident