Find the limit using the graph of f ( x ) f\left(x\right) f ( x ) shown. lim x → − 2 f ( x ) \lim_{x\rarr-2}f\left(x\right) lim x → − 2 f ( x )

Here, we're asked to find the limit using the graph of f of x shown below. Now here, the limit that we're asked to find is the limit of f of x, our function, as x approaches negative 2. So let's go ahead and take a look at our graph here. And we wanna look at what our graph is doing when x is getting really, really close to negative 2 from either side. So first coming in from that left side getting really, really close to negative 2, I see that my function seems to be approaching a value of negative 3. Then coming in from that right side, I see the same thing happening. As we're getting really, really close to that x value of negative 2 here, we seem to be approaching negative 3 on our function. So here, the limit of f of x as x approaches negative 2 is equal to negative 3. Now something that might be a bit confusing here is that if we look at the actual value of our function at negative 2, it seems to be equal to 4 because there's a hole on our graph and it sort of jumps up there like a piecewise function might. Now that doesn't matter here because remember that a limit is looking at our values, getting really, really close as x is approaching our value of negative 2, not when x is negative 2. So it doesn't matter that the actual value of our function here is 4. Our limit is still negative 3. Let me know if you have any questions there, and I'll see you in the next one.

1. Limits and Continuity

Introduction to Limits

Calculus

1. Limits and Continuity

Introduction to Limits

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Multiple Choice

Find the limit using the graph of $f\left(x\right)$ shown.
$\lim_{x\rarr-2}f\left(x\right)$

$4$

$-2$

$-3$

Unable to determine

Verified step by step guidance

Identify the point on the graph where x approaches -2. Notice that there is a hole in the graph at x = -2, indicating that the function is not defined at this point.

Observe the behavior of the graph as x approaches -2 from the left. The y-values of the function appear to approach a certain value.

Similarly, observe the behavior of the graph as x approaches -2 from the right. The y-values of the function also appear to approach the same value as from the left.

Since the y-values from both the left and right sides of x = -2 approach the same value, the limit exists at this point.

Determine the y-value that the function approaches as x approaches -2 from both sides. This y-value is the limit of the function as x approaches -2.

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Struggling with Calculus?

Find the limit using the graph of f(x)f\left(x\right)f(x)shown.limx→−2f(x)\lim_{x\rarr-2}f\left(x\right)limx→−2f(x)

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Introduction to Limits practice set

Find the limit using the graph of $f\left(x\right)$ shown.
$\lim_{x\rarr-2}f\left(x\right)$