Find the limit using the graph of f ( x ) f\left(x\right) f ( x ) shown. lim ⁡ x → 4 f ( x ) \lim_{x\rarr4}f\left(x\right) lim x → 4 f ( x )

In this problem, we're asked to find the limit using the graph of f of x shown below. Now here we're specifically asked to find the limit of f of x as x approaches 4. So looking at our graph here, we want to look at what our function is doing as x gets really, really close to a value of 4. So looking at my graph here coming in from that left side, as x gets really, really close to 4, I see that my function seems to be approaching a value of negative 2. Then coming in from the other side, I see the same thing. As x gets really, really close to 4, my function seems to be approaching a value of negative 2. So here the limit of f of x as x approaches 4 is equal to negative 2. Now a mistake that you might have made here is thinking that we don't even have a limit here because there's a hole in our graph. Now it's easy to get tripped up by that the first time you see it. But remember that it doesn't matter what the value of our function is at 4, but just what it's doing as x approaches 4 as it gets really, really close to it but isn't actually equal to it. So it doesn't matter that our graph isn't actually defined for our x value of 4. It just matters that as x gets really close to 4, our function is approaching a value of negative 2, and that's all there is to it. Let me know if you have any questions there, and I'll see you in the next one.

22. Limits & Continuity

Introduction to Limits

Precalculus

22. Limits & Continuity

Introduction to Limits

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Multiple Choice

Find the limit using the graph of $f\left(x\right)$ shown.
$\lim_{x\rarr4}f\left(x\right)$

$2$

$-2$

$0$

Unable to determine

Verified step by step guidance

Observe the graph of the function f(x) and identify the behavior of the function as x approaches 4 from both sides.

Notice that as x approaches 4 from the left (x < 4), the function values are decreasing and approaching a certain value.

Similarly, as x approaches 4 from the right (x > 4), the function values are also approaching the same value.

The limit of f(x) as x approaches 4 is the value that the function approaches from both sides, regardless of the actual value of f(4).

From the graph, determine the y-value that the function approaches as x approaches 4, which is the limit of f(x) as x approaches 4.

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Struggling with Precalculus?

Find the limit using the graph of f(x)f\left(x\right)f(x) shown.lim⁡x→4f(x)\lim_{x\rarr4}f\left(x\right)limx→4​f(x)

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Find the limit using the graph of $f\left(x\right)$ shown.
$\lim_{x\rarr4}f\left(x\right)$