Continuity Exploration Assignment

The following questions relate to [b]continuity of a function f at an input value [i]x[/i] = a. [/b][br][br]For the definition of a function to be continuous at any input value, please refer to [url=https://www.geogebra.org/m/xeA7M94B]this worksheet[/url] first.

Graph for Question 1

1) Why is this function not continuous at x = a? (Slide the dot to change the graph.)

Graph for Question 2

2) Why is this function not continuous at x = a? (Slide the dot to change the graph.)

Graph for Question 3

3) Why is this function not continuous at x = a? (Slide the dots to change the graph.)

4) Which one of these functions is NOT continuous at x=0 because f(x) is not defined at x=0?

(a) [math]f\left(x\right)=\frac{1}{x}[/math] [table][tr][td](c) f(x)= -1, [math]x\le0[/math][/td][/tr][tr][td] = 1, x>0[/td][/tr][/table] (b) [math]f\left(x\right)=|x|[/math] [table][tr][td](d) f(x)= x, [math]x\ne0[/math][/td][/tr][tr][td] = 1, x=0[/td][/tr][/table]

5) Which one of these functions is NOT continuous at x=0 because the limit as x->0 of f(x) does not exist?

[table][tr][td](c) f(x)= -1, [math]x\le0[/math][/td][/tr][tr][td] = 1, x>0[/td][/tr][/table] [table][tr][td](d) f(x)= x, [math]x\ne0[/math][/td][/tr][tr][td] = 1, x=0[/td][/tr][/table] (b) [math]f\left(x\right)=|x|[/math] (a) [math]f\left(x\right)=\frac{1}{x}[/math]

6) Which one of these functions is NOT continuous at x=0 because the limit as x->0 of f(x) does NOT equal f(a)?