Use the graph of f(x) = x / (x² − 2x − 3)²

Question

Use the graph of f(x) = x / (x² − 2x − 3)² to determine lim x→−1 f(x) and lim x→3 f(x).

Accepted Answer

Hi everyone, let's take a look at this practice problem dealing with limits. This problem says determine the limit as x approaches minus 4 of G of X and the limit as X approaches 2 of G of X by using the graph of G of X is equal to minus x divided by the quantity of X2 plus 2X minus 8 in quantity squad. While the question we're given a graph of our function G of X. We're also give 4 possible choices as our answers. For choice A, we have the limit as x approaches minus 4 of G of X is equal to infinity, and the limit as X approaches 2 of G of X is equal to minus infinity. For choice B, we have the limit as X approaches minus 4 of G of X is equal to minus infinity, and the limit as X approaches 2 of G of X is equal to infinity. For choice C, we have the limit as X approaches minus 4 of G of X is equal to minus infinity, and the limit as X approaches 2 of G of X is equal to 0. And for choice D, we have the limit as X approaches minus 4 of G of X is equal to 0, and the limit as X approaches 2 of G of X is equal to minus infinity. So, the question wants us to use our graph to determine the two limits, the limit as X approaches minus 4, and the limit as X approaches 2 of our function G of X. So, let's start off by looking at the limit as X approaches minus 4. And so if we look at our graph, our function G of X is approaching an arbitrarily large positive value from both sides of X is equal to -4. So, since it's approaching an arbitrary large positive value, that means that the limit As X approaches -4 of G of X. It's going to be equal to infinity. We'll do something similar for our limit as x approaches too. If we look at how our function. is behaving at X equal to 2, we see that our function G of X is approaching an arbitrarily large negative value as X approaches 2. That means that the limit as X approaches 2 of G of X. It's going to be equal to minus infinity. So, these are the two values for our limits that we are looking for. And if we come down to our answer choices. It looks like the correct answer choice corresponds to answer choice A. So I hope that this explanation has been useful, and I'll see you in the next video.

Use the graph of f(x) = x / (x² − 2x − 3)² to determine lim x→−1 f(x) and lim x→3 f(x).

Key Concepts

Limits

Continuity

Asymptotes

Watch next

Use the graph of f(x) = x / (x2 − 2x − 3)2 to determine lim x→−1 f(x) and lim x→3 f(x).

Key Concepts

Limits

Continuity

Asymptotes

Watch next

Use the graph of f(x) = x / (x² − 2x − 3)² to determine lim x→−1 f(x) and lim x→3 f(x).