Find the limit using the graph of f ( x ) f\left(x\right) f ( x ) shown. lim x → 1 f ( x ) \lim_{x\rarr1}f\left(x\right) lim x → 1 f ( x )

Here we're asked to find the limit using the graph of f of x, our function that is shown below. And the limit that we're asked to find here based on our graph is the limit of f of x as x approaches 1. Now looking at our graph here, this is our function f of x and we specifically are looking at our function as x approaches 1, meaning that we wanna look at values that are getting a really, really close to 1 from either side and kind of observe what our function is doing at that point. Now as we're getting really, really close to 1 coming in from this left side, I see that my function is getting close to a value of 2. Then coming in from that right side, I see the same thing that my function is getting really close to a value of 2. Now that tells us that our limit of f of x as x approaches 1 here is simply equal to 2, and we're all done here. Let me know if you have any questions, and I'll see you in the next one.

22. Limits & Continuity

Introduction to Limits

Precalculus

22. Limits & Continuity

Introduction to Limits

Struggling with Precalculus?

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Multiple Choice

Find the limit using the graph of $f\left(x\right)$ shown.
$\lim_{x\rarr1}f\left(x\right)$

$2$

$1$

$0$

Unable to determine

Verified step by step guidance

Identify the point on the x-axis where the limit is to be evaluated, which is x = 1.

Observe the behavior of the function f(x) as x approaches 1 from the left (x -> 1^-).

Observe the behavior of the function f(x) as x approaches 1 from the right (x -> 1^+).

Check if the values from the left and right approaches are the same. If they are, the limit exists and is equal to this common value.

From the graph, determine the y-value that the function approaches as x approaches 1 from both sides.

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Struggling with Precalculus?

Find the limit using the graph of f(x)f\left(x\right)f(x)shown.limx→1f(x)\lim_{x\rarr1}f\left(x\right)limx→1f(x)

Watch next

Introduction to Limits practice set

Find the limit using the graph of $f\left(x\right)$ shown.
$\lim_{x\rarr1}f\left(x\right)$