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Below is the graph of $f(x) = \dfrac {-x^3-x^2+6x}{5x+15}$ .

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

(a) $f(-3)$ is defined (b) $\lim \limits _{x \to -3} f(x)$ exists (c) $\lim \limits _{x \to -3} f(x) = f(-3)$ Both (a) and (b) are true. (a), (b), and (c) are true.

Consider the piecewise function defined by $f(x) = \begin {cases} x^2-3 & \textrm {for } x \leq 2 \\ 2x+a & \textrm {for } x >2 \end {cases}$ Which value for $a$ makes the function $f$ continuous?

-3 1 2 3 4

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

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

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

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

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

Yes No I need more information to answer the question.