Continuity

One of the conditions a function must satisfy to be continuous at a number is "f(c) must exist"

• TRUE

• FALSE

At x=a there is a _________ discontinuity.

Which of the following best describes the continuity at x = 2?

• Jump Discontinuity

• Removable Discontinuity

• Continuous

• Infinite Discontinuity

Which of the following best describes the continuity at x = 1?

• Continuous

• Removable Discontinuity

• Infinite Discontinuity

• Jump Discontinuity

At which x-value is there a jump discontinuity?

• $x=-3$

• $x=-6$

• $x=1$

• $x=2$

Which of the following best describes the continuity at x = -4?

• Continuous

• Removable Discontinuity

• Infinite Discontinuity

• Jump Discontinuity

Is f(x) continuous at x = a, and why?

• No, $\lim_{x\rightarrow a^-}f\left(x\right)\ne\lim_{x\rightarrow a^+}f\left(x\right)$

• No, $\lim_{x\rightarrow a}f\left(x\right)\ne f\left(a\right)$

• Yes, $\lim_{x\rightarrow a^-}f\left(x\right)=\lim_{x\rightarrow a^+}f\left(x\right)$

• Yes, $\lim_{x\rightarrow a}f\left(x\right)=f\left(a\right)$

At x = 1 there is a _______ discontinuity.

Is the function continuous at x = 2, and why?

• Yes, $\lim_{x\rightarrow2}f\left(x\right)=f\left(2\right)$

• Yes, $\lim_{x\rightarrow2^-}f\left(x\right)=\lim_{x\rightarrow2^+}f\left(x\right)$

• No, $\lim_{x\rightarrow2^-}f\left(x\right)\ne\lim_{x\rightarrow2^+}f\left(x\right)$

• No, $\lim_{x\rightarrow2}f\left(x\right)\ne f\left(2\right)$

A function is continuous on a number if and only if f(c) = lim f(x) as x approaches a number c.

• TRUE

• FALSE