# Thread: dis/continuous function - Sketch Graph

1. ## dis/continuous function - Sketch Graph

Hello,
how can I sketch the Graph of the following function?
----------4 x < 2
f(x) = {
----------x² 2 ≤ x

and I've to know if this function is continuous or not but I think that I can solve this after sketching the function ?

Infi

2. Originally Posted by Infi
Hello,
how can I sketch the Graph of the following function?
----------4 x < 2
f(x) = {
----------x² 2 ≤ x

and I've to know if this function is continuous or not but I think that I can solve this after sketching the function ?

Infi
Hi Infi,

$f(x) = \left \{\begin {array}{cc}4, & \mbox{ if } x < 2 \\ x^2, & \mbox{ if } x \ge 2 \end {array}\right$

This is a piecewise function. The first branch is a horizontal line at F(x) = 4 for all x less than 2. f(2) is not defined on this branch.

The second branch is the right branch of a parabola starting at f(x) = x^2 for all x greater than or equal to 2.

Since the second branch includes f(2) = 4, the function is continuous for all values of x.