Calculus: for what x-values is the function not continuous

[sareevan]

List all the x-values for which the following functions are NOT continuous.

f(x) = {x^3 if x≤2
. . . . .{8 if x>2

f(x) = {x+3 if x<0
. . . . .{-x+1 if x≥0

 

[stapel]

So you've graphed the functions, and... then what? Where are you stuck?

Please reply with specifics. Thank you.

Eliz.

 

[sareevan]

calculus

I graphed the functions, but I came up x=0, and continuous everywhere else. I need to know if I'm on the right path.

 

[stapel]

I came up x=0, and continuous everywhere else.

For which function?

Why do you think you're wrong?

Please be specific, and include your answer for the other function as well.

Thank you.

Eliz.

 

[sareevan]

Calculus

List all the x-values for which the following functions are NOT continuous.

f(x) = {x^3 if x≤2
{8 if x>2

I got x=0, and continuous everywhere else when I graphed the function. My teacher wrote that it was wrong on my paper.

f(x) = {x+3 if x<0
{-x+1 if x≥0

I got all numbers were continuous when I graphed this function, but my teacher wrote that it was wrong on my paper.

 

[stapel]

Why would you think that the first function would be discontinuous at x = 0? The function x³ is continuous, and the piecewise function does not break at x = 0. Please reply with your reasoning.

If you thought that the second function was continuous, then you must have graphing the pieces incorrectly, because they shouldn't have joined up at the ends. Try graphing the two pieces again.

Eliz.