Continuity Exploration

The following questions relate to [b]continuity of a function f at an input value [i]x[/i] = a. [/b][br][br]If you need a refresher on what it means for a function to be continuous at any input value, refer to [url=https://www.geogebra.org/m/xeA7M94B]this worksheet[/url].

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 of the functions below is NOT continuous at x=0 because of the reason in Question 1?

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

5) Which of the functions below is NOT continuous at x=0 because of the reason in Question 2?

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

6) Which of the functions below is NOT continuous at x=0 because of the reason in Question 3?

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

7) Which of the functions below IS continuous at x=0?