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 = 4 c=4 c = 4

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 our function when x is equal to 4 because that's our specified c value. Now looking at our graph here, we can go ahead and just test if this is continuous or not by tracing our function on our graph. Now if I try to trace my function here as I get to x equals 4, I do have to pick up my pen, put it somewhere entirely put it entirely somewhere else, and then continue on. Now because I couldn't just continuously trace with my pen, I know that this function is discontinuous at x equals 4 and I could further verify this numerically by finding that my limit here is actually equal to 1 while my function value is equal to 4. Now these 2 are not the same so that further proves that my function is discontinuous. 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 $x=c$ .
$c=4$

Continuous

Discontinuous

Verified step by step guidance

Identify the point of interest on the graph, which is at x = 4.

Examine the graph at x = 4 to see if there is a break, jump, or hole in the graph. A function is continuous at a point if the graph is unbroken at that point.

Check if the limit of f(x) as x approaches 4 from the left (x -> 4-) is equal to the limit of f(x) as x approaches 4 from the right (x -> 4+).

Determine if the value of the function at x = 4, f(4), is equal to the common limit found in the previous step.

Conclude that the function is discontinuous at x = 4 if there is a break, jump, or if the limits from the left and right do not equal f(4).

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=4c=4c=4

Watch next

Continuity practice set

Use the graph of $f\left(x\right)$ to determine if the function is continuous or discontinuous at $x=c$ .
$c=4$