Use the graph of f ( x ) f\left(x\right) f ( x ) to determine if the function is continuous or discontinuous at x = c x=c x = c . c = 3 c=3 c = 3

Here we want to use the graph of f of x to determine if our function is continuous or discontinuous at x equals c. Now here we're looking at where x is equal to 3 because that's our specified value of c. Now looking at my graph here, if I were to go ahead and trace my function where x is equal to 3, I see that I would have to pick up my pen and move it to a different place as x is c. So I know that I actually have an asymptote here, meaning that this function is a discontinuous. Now because we just did this by tracing our graph and verifying that we had to lift our pen, you may also be asked to actually verify this using values which you could easily do by finding your limit and your function value. Now here our limit as x approaches 3 of this function actually does not exist because we have unbounded values and our function value also doesn't exist. So here our function is discontinuous due to this asymptote here. Thanks for watching and let me know if you have questions.

1. Limits and Continuity

Continuity

Calculus

1. Limits and Continuity

Continuity

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Multiple Choice

Use the graph of $f\left(x\right)$ to determine if the function is continuous or discontinuous at $x=c$ .
$c=3$

Continuous

Discontinuous

Verified step by step guidance

Identify the point of interest on the graph, which is at x = 3.

Observe the behavior of the function as it approaches x = 3 from both the left and the right.

Check if the function has a defined value at x = 3 by looking for a filled dot on the graph at this point.

Determine if the left-hand limit and the right-hand limit as x approaches 3 are equal.

Conclude whether the function is continuous or discontinuous at x = 3 based on the presence of a jump, hole, or asymptote at this point.

5:34m

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Go to Practice

Struggling with Calculus?

Use the graph of f(x)f\left(x\right)f(x) to determine if the function is continuous or discontinuous at x=cx=cx=c.c=3c=3c=3

Watch next

Continuity practice set

Use the graph of $f\left(x\right)$ to determine if the function is continuous or discontinuous at $x=c$ .
$c=3$