Question

Sketch the graph of function f and evaluate lim f(x) if it exists for the given value of a. (a=1)
f(x)={x if x <1
{0 if x = 1
{- x+2 if x>1

Answer 1

\(y=x\) is a line, as is \(y=-x+2\) it is \(y=x\) to the left of 1, and \(-x+2\) to the right

Answer 2

if you replace \(x\) by 1 you see you get the same number in both expressions, \(y=1\) and also \(y=-1+2=1\) so the limit is 1, even though the value of the function at 1 is \(f(1)=0\)

Answer 3

I don't understand the if x <1, x=0, x>1 part? What does it mean? If a=1 doesn't it mean put 1 in for x? @satellite73