If the slope of a line is vertical (undefined) does that mean that it is discontinuous at that point?

Question

the graph itself looks like a staircase pattern, i had to draw the graph on the interval from 1-2 then point out the discontinuity, at x=1 and x=2 there are vertical lines (hence the staircase pattern). I thought it would be discontinuous there??

Answer 1

it does not mean that the graph is discontinuous at that point, it just means its derivative is undefined. A good example of this is the tangent line to the graph y=x^(1/3), at x=0,which is vertical, but the graph itself is defined.

Answer 2

No.. Take the equation
X+3
----------
X-5

At x=5, the curve is discontinuous because division by zero is undefined.

But the slope of the line X=5 is vertical, but not discontinuous.

Answer 3

This would need some checks
Do you know the definition of continuity?Im me for a discussion if u do