I have two problems.. I'll put them both here, and show my work on both of them.(adsbygoogle = window.adsbygoogle || []).push({});

1. Is this function continuous on [-1, 1]?

f(x) =

x / |x| , x does not equal 0

0 , x = 0

After graphing this function, the first statement gives y = -1 for all x < 0, and y = 1 for all x > 0. The second statement makes y = 0 when x = 0. Putting everything together, y values are defined at -1, 0, 1, but nothing in-between. Does this make the function not continuous because of the jumping at x = 0?

2.

Discuss the continuity of the function g:

g(x) =

sin x / x , for x does not equal 0

1/2 , for x = 0

There is a hole in the graph at x = 0 (for the first statement), but the second statement defines x = 0 to be 1/2, it's just lower than the curve in the first statement. Would this be a continuous function or not?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Continuity with piecewise functions.

**Physics Forums | Science Articles, Homework Help, Discussion**